QUIZZES after midterm1 Flashcards
Which of the following is NOT one of the assumptions of hypothesis testing
a) The independent variable is measured on an interval scale
b) Participants are randomly selected from the population
c) The dependent variable is measured on an interval scale
d) The population distribution is approximately normal
A)
Only the dependent variable is required to be on a scale variable to meet our assumptions.
A distribution of z scores has a known mean and standard deviation. What are they?
a) Mean = 0, SD = 1
b) Mean = 100, SD = 15
c) Mean = 50, SD = 1
d) Mean = 1, SD = 0
A)
For our standard z distribution, our mean is always zero and our standard deviation is always 1. In this way, we can use our z distribution to look at z scores.
THESE are inferential statistical analyses based on a set of assumptions about the population.
a) nonparametric tests
b) parametric tests
c) standardized tests
d) nonstandardized tests
B)
A researcher hypothesizes that there is a significant relationship between stress and fatigue. Specifically, he hypothesizes that as stress increases, fatigue levels will also increase. This example best illustrates what type of hypothesis test?
a) null hypothesis test
b) one-tailed test
c)nondirectional test
d)two-tailed test
B)
The critical values associated with a p level of 0.05 for a two-tailed hypothesis test using the z statistic are:
a) +1.96
b) -1.96 and + 1.96
c) -1.65 and +1.65
d) +1.65
B)
Since this value is BEYOND the critical p value of 1.96, we would reject the null hypothesis. (Recall that we never support the alternative hypothesis.)
See also Chapter 7 Step 6: Make a Decision
Using a p level of 0.05 and cutoff values of z = +1.96 and z = –1.96, what decision would we make if our calculated z statistic was 1.97?
a) fail to reject the null hypothesis
b) reject the null hypothesis
c) support the null hypothesis
d) support the alternative hypothesis
B)
The p level is the:
a) probability with which a test statistic would occur if the null hypothesis were true.
b) cutoff probability at which a test statistic is considered extreme.
c) probability with which a test statistic would occur if the research hypothesis were true.
d) probability with which a test statistic would occur if both the null and research hypothesis were false.
A)
Note that we are doing a test of the NULL hypothesis. Since we are using the NULL hypothesis (or in this case, our population mean and standard deviation) to develop our comparison distribution, the p value indicates how likely that value would be found if the null hypothesis were true. We usually use a 5% cut-off; thus, we only accept the value to be found 5% at chance. See also Chapter 7 The Six Steps of Hypothesis Testing.
How does the sampling distribution of means for a sample with N = 5 differ from that of a sample with N = 100?
a) Both sampling distributions will be identical; they will not differ.
b) The mean of the sampling distribution of means with N = 5 will be closer to the mean of the population than the mean of the sampling distribution with N = 100.
c) There is more variance in the sample distribution with N =5 than with N = 100.
d) There is less variance in the sampling distribution with N = 5 than with N = 100.
C)
This question goes back to the Central Limit Theorem discussed in Chapter 6. The more data points in your sample, the less variability there will be in the sampling distribution. This is because the formula for the standard error is:
The higher N is, the smaller the standard error will be. It’s math :)
A(n) _ is based on our sample statistic; it conveys the range of sample statistics we could expect if we conducted repeated hypothesis tests using samples from the same population.
a) coefficient of determination
b) point estimate
c) interval estimate
d) estimated standard error
C)
This is the definition for an interval estimate as described in the section on Chapter 8 Confidence Intervals. They generally add and subtract a value that is our margin of error (the size of which depends on how confident we want to be!).
Which two figures below would produce larger effect sizes?
C) & D)
Look at the overlap – more overlap, less effect size.
Less overlap, a larger effect size.
THIS is a measure of our ability to reject the null hypothesis given that the null hypothesis is false.
a) R squared
b) Cohen’s d
c) Statistical power
d) Eta squared
C)
Statistical power is used to calculate how likely we are to reject the null hypothesis give it is false. These calculations are completed before you complete a study to see if you have the resources available to get enough participants in your study to find a significant effect, if one exists. See Chapter 8: Statistical Power.
Imagine The California Verbal Learning Test has a national average of 14.68 items recalled with a standard deviation of 2.01 items. A researcher administers the test to 24 patients with early onset Alzheimer’s Disease. They score an average of 8.5 items recalled. What would be the standard error for the comparison distribution? (Round to two decimal places)
0.41
Imagine that a self-esteem scale has an average of 91.60 and a standard deviation of 14.76. What is the score of a person who obtains a z score of -0.47? (Round to two decimal places)
84.66
Imagine that you are a tennis player. You calculate the number of points you get each game in order to determine how much your points change from game to game. What measure should you calculate?
THE MODE
THE MEDIAN
THE MEAN
THE STANDARD DEVIATION
STANDARD DEVIATION
Luca would like to determine the probability a person at Langara has brown hair. They sit in the cafeteria and every time a person walks in, they record their hair colour. The hair colours recorded are: 24 blonde, 58 brown, and 17 red. Using the data, what is the probability someone at Langara will have brown hair (rounded to two decimal places)?
0.59
Two students take a math test at two different high schools. Tim scores 50. His class’s average was 40 with a standard deviation of 5. Mira scores 25. Her class’s average was 21 with a standard deviation of 2. Who scored higher on the test?
Tim scored higher than Mira
Mira scored higher than Tim
Tim and Mira scored equally high
We are unable to compare test scores from different tests
TIM AND MIRA SCORED EQUALLY HIGH
You have completed a study in which people were randomly assigned to consume either no caffeine, 100 mg of caffeine, or 200 mg of caffeine. You then measure their reaction time. What type of graph should you use to visually display this data?
A BAR GRAPH
A researcher is looking at SES (low, medium, and high). Which measure of central tendency should he use for this data?
Mode
Median
Mean
Range
MODE
A researcher collects some data on the relationship between introversion and academic success. The researcher finds that, contrary to their hypothesis, there was no relationship between introversion and CGPA. She does, however, find that there is a relationship between introversion and retention rates. Despite this not being her original focus, she publishes the finding as though this was the intent of the study. This is an example of:
HARKing
You and your friends decide to complete the Narcissism Personality Inventory. You find the following values: 11, 19, 12 and 24. What is the mean value? (Round to two decimal places)
16.5
Below is a histogram looking at the frequency of test scores. Which of the following statements is correct:
The mean is higher than the median
The mean, median, and mode are approximately the same value
The mean is lower than the median
The mode is higher than the mean
THE MEAN IS HIGHER THAN THE MEDIAN
You obtain the weights of all of the students in your data analysis class. The scores range from 43 to 95 kilograms. Based on the guidelines set out in this course, which of the following intervals in a frequency table makes the most sense for your data?
40 to 42.9 kg
50 to 69.9 kg
50 to 59.9 kg
40 to 69.9 kg
50 TO 59.9
A standardized test contains a mean of 25 with a standard deviation of 5. If Harry scores 30 on the test, what is his percentile?
84%
You develop a test that measures social anxiety. The test is scored from 0 to 120, with higher scores representing higher social anxiety. You give the test to a patient that has high social anxiety. The first week they score 110, the second week they score 112, and the third week they score 111. The results suggest that the test is:
RELIABLE
NEITHER RELIABLE NOR VALID
VALID
BOTH RELIABLE AND VALID
BOTH
You receive a dataset of memory performance with the following values: 6, 10, 8, 1, 16, 14. Calculate the Interquartile range (IQR).
8
You measure the number of hours a child watches violent television each week. You get the following values: 14, 3, 15, 7, 2. Calculate the variance. (Round to two decimal places)
29.36
Imagine this following image was created to demonstrate the change in home sales over time:
What ‘lie’ is represented by this image?
INACCURATE VALUES LIE
A researcher plans to explore whether the amount of marijuana a woman smokes during pregnancy is related to fetal weight. What type of study should the researcher use?
correlational study
within-groups experiment
between-groups experiment
double-blind experiment
CORRELATION STUDY
A provincial survey is given to every student in BC. The students report studying a mean of 11.00 hours per week with a standard deviation of 5.18. Min’s class of 38 students studies an average of 9.34 hours per week. What is the z statistic for Min’s class? (Round to two decimal places
-1.98
Past research has shown that words presented in red background are better remembered that words presented in a neutral background (Mehta & Zhu, 2009). A researcher would like to know if this finding extends to math performance. She places signs around campus asking participants to participate in her study for $10. Participants are assigned to complete math questions with either a red or neutral background. They researcher finds that those who read the questions with a red background scores an average of 25 questions correct, whereas those with the neutral background scored an average of 21 questions correct. The difference was not statistically significant.
Answer the following:
a. Explain how the type of sampling used in the study affects the generalizability of the study. (1 point)
b. Identify the control and experimental groups. (1 point)
c. What is the null hypothesis? (1 point)
d. What is the research hypothesis? (1 point)
e. What decision should the researcher make and why? (1 point)
f. Given your answer in e), what type of error might the researcher have made? Explain your answer. (1 point)
a) if ppl are paid, then it’s not random sampling. It’s an incentive to participate.
c) There is no statistical difference between the two backgrounds.
d) There is a diffeence in the background scores.
MY ANSWERS:
a) if ppl are paid, then it’s not random sampling. It’s an incentive to participate.
c) There is no statistical difference between the two backgrounds.
d) There is a diffeence in the background scores
CORRECT ANSWERS:
A researcher wishes to explore how stereotype threat can influence math performance in college women. 112 college students identifying as women are asked to complete a math test. The math test consists of 45 multiple choice questions. One group is placed in a testing room with 4 confederates who are all men. The other group is placed in a testing room with confederates, 2 of whom are men and 2 are women. The researcher finds that the average score on the test is 32 for the women who complete the test in the presence of men and 38 for the women who complete the test in the presence of men and women. A statistical analysis suggests that the women who completed the test in the presence of only men performed worse than those who completed the test in the presence of both men and women.
Answer the following:
a. Who is the population? Who is the sample? (1 point)
b. What are the independent and dependent variables? (1 point)
c. What are the levels of the independent variable? (1 point)
d. Identify whether the dependent variable is nominal, ordinal, interval or ratio and if it is continuous or discrete. Explain your answers. (2 points).
e. Is this a between- or within-group design? How do you know? (1 point)
f. Do you think random sampling was used? Explain your answer. (1 point)
g. Do you think random assignment was used? Explain your answer. (1 point)
h. Explain how both descriptive and inferential statistics are represented in this example. (2 points)
MY ANSWERS:
a) pop = all college women (who can do math, maybe?) sample = just the 112 women
b) indep = the confederates dep = score of the math test
c) 2 groups of confederates (one is all men, other is half/half)
d) ratio + continuous ( ratio has a true zero and the scores could have decimal points)
e) between groups. two groups assigned to two testing groups
f) not random as it was chosen from a group specifically identifying as women. should have been randomly chosen
g) there’s not enough data to say this fro certain
h) descriptive = describes the group who identify as women (112) / inferential = it would have to be applied to the population of all the women of the college.
CORRECT ANSWERS:
A researcher wishes to explore how stereotype threat can influence math performance in college women. 112 college students identifying as women are asked to complete a math test. The math test consists of 45 multiple choice questions. One group is placed in a testing room with 4 confederates who are all men. The other group is placed in a testing room with confederates, 2 of whom are men and 2 are women. The researcher finds that the average score on the test is 32 for the women who complete the test in the presence of men and 38 for the women who complete the test in the presence of men and women. A statistical analysis suggests that the women who completed the test in the presence of only men performed worse than those who completed the test in the presence of both men and women.
**Answer the following: **
a. Who is the population? Who is the sample? (1 point)
b. What are the independent and dependent variables? (1 point)
c. What are the levels of the independent variable? (1 point)
d. Identify whether the dependent variable is nominal, ordinal, interval or ratio and if it is continuous or discrete. Explain your answers. (2 points).
e. Is this a between- or within-group design? How do you know? (1 point)
f. Do you think random sampling was used? Explain your answer. (1 point)
g. Do you think random assignment was used? Explain your answer. (1 point)
h. Explain how both descriptive and inferential statistics are represented in this example. (2 points)
MY ANSWERS:
a) pop = all college women (who can do math, maybe?) sample = just the 112 women
b) indep = the confederates dep = score of the math test
c) 2 groups of confederates (one is all men, other is half/half)
d) ratio + continuous ( ratio has a true zero and the scores could have decimal points)
e) between groups. two groups assigned to two testing groups
f) not random as it was chosen from a group specifically identifying as women. should have been randomly chosen
g) there’s not enough data to say this fro certain
h) descriptive = describes the group who identify as women (112) / inferential = it would have to be applied to the population of all the women of the college.
TEACHER ANSWERS:
MY ANSWERS:
a) 17
b) 2/40 = 0.05 = 5%
c) 35.75
d) definitely negatively skewed – more distributed towards the right side of the graph (more towards the higher numbers)
CORRECT ANSWERS:
All of the grade 8 students across Vancouver are given a reading comprehension test. The mean score is 56 with a standard deviation of 12. Interestingly, the distribution of scores appears to be slightly negatively skewed. A teacher claims his 22 students outperformed the other classes in Vancouver due to her teaching methods. His class scored 58 on the test with a standard deviation of 8.
Answer the following:
a. Is the value 12 a statistic or a parameter? Explain your answer. (1 point)
b. If the teacher wished to compare his students to the average score, what type of distribution would he need to use? Explain your answer. (1 point)
c. What would be the mean of the distribution? How do you know? (1 point)
d. Do you think his comparison distribution would be normal, positively skewed or negatively skewed? Explain your answer. (1 point)
MY ANSWERS:
A) it’s a parameter as it describes the whole population of grade 8 students in Vancouver.
B) The average score would be the ‘mean’, so he would need to compare against the distribution of means graph.
C) the mean of the distribution would be the same as the whole population of Grade 8 students (56).
D) As in, his 1 singular classroom? It would be very slightly neg scored. The distribution of means should be normally distributed as there would be many, many scores to base it off.
CORRECT ANSWERS:
a. The value of 12 is a parameter (0.5), since it has been measured for every grade 8 student in the region (the population of interest) (0.5)
b. He would need to use a distribution of means, since he would like to compare the score of his 22 students (a mean) to an average score.
c. The mean would be 56. The CLT tells us the mean of the distribution = the mean of the population (1 point)
d. Normal. Since the sample size is 22, even if the underlying distribution is slightly skewed, due to the CLT the comparison distribution should be normal. -.25 clarify CLT makes it normal
QUIZ WEEK 6:
Which of the following is an example of p-hacking?
a) A researcher fabricates some results to support their hypothesis
b) A researcher replicates their study using a new sample of participants
c) A researcher changes their hypothesis after analyzing their data
d) A researcher collects six dependent measures but only reports on the two that show significant results
D)
P-hacking refers to the practice of selectively analyzing data or manipulating statistical tests in order to obtain significant results or support a desired hypothesis. By collecting multiple dependent measures but only reporting on the ones that yield significant results, the researcher is engaging in p-hacking. This selective reporting can lead to a biased presentation of the findings and can be misleading.
WEEK 6 QUIZ:
According to a “how to stop bullying” website, 15 percent of students report experiencing bullying one to three times within the most recent month. Assume the standard deviation is 5 percent of students. Joseph collects data from 125 students at a medium-sized school in Iowa and finds that only 12 percent reported this rate of bullying. What is his 95 percent confidence interval (rounded to two decimal places)?
[11.12, 12.88]
[14.27, 15.73]
[11.33, 12.67]
[14.12, 15.88]
[11.12, 12.88]
A teacher is comparing her students’ performance to the IQ test. Recall that the IQ test has a mean of 100 and a standard deviation of 15. If the teacher’s class consists of 30 students, and her students score a value of 105 on the IQ test, what would be the effect size (rounded to two decimal places)?
0.33
- use Cohen’s d formular:
- d=M-mu/standard deviation
- d=105-100/15
- =0.33
QQQQQQQQQQQQQQQQQQ
Miranda is completing a z test. She would like to use a one-tailed test with a p level of 0.05. What is her critical z value(s)?
1.96
-1.645 and 1.645
-1.645 or 1.645
-1.96 or 1.96
C) -1.645 OR +1.645 (BECAUSE IT’S DIRECTIONAL)
For a one-tailed test with a p level of 0.05, the critical z-value can be found using the standard normal distribution. Since the test is one-tailed, we need to consider only one tail of the distribution.
If the alternative hypothesis is directional (e.g., greater than or less than), the critical z-value will be either -1.645 or 1.645.The alternative hypothesis is Ha and it’s the ‘research hypothesis’.
If the alternative hypothesis is non-directional (e.g., not equal to), the critical z-value will be -1.96 or 1.96.
Since the question does not specify the direction of the alternative hypothesis, we assume a non-directional (two-tailed) test. Therefore, the correct answer is:
-1.96 or 1.96
These critical z-values correspond to a significance level of 0.05 for a two-tailed test.Regarding the calculation of critical z-values, they are determined based on the desired significance level (α) and the type of test (one-tailed or two-tailed). The critical z-value(s) represent the cutoff point(s) beyond which the test statistic would be considered statistically significant.
To calculate the critical z-value(s), you need to consult a standard normal distribution table
A researcher conducts a study on a volunteer sample of 45 first-year students, exploring the effect of white noise on attention. Her measure of attention is based on correct identifications of targets, with possible scores ranging from 0 to 65. Which of the following assumptions should she be most concerned about?
a) The distribution of the population is approximately normal.
b) Participants were randomly sampled from the population.
c) The dependent variable is assessed using a scale variable.
d) Both b) and c)
B)
In one statistics course, the average score on their quiz is 62.04 points with a standard deviation of 5.43. If Amy scores 58, what percentage of students scored BETTER than Amy (rounded to two decimal places)?
27.04
22.96
77.04
72.96
77.04
A teacher would like to compare her classes standardized English scores to the population. This test has a mean of 100 and a standard deviation of 12. Her class consists of 34 students and they scored 110 on the test with a standard deviation of 10. Based on this information, what value should the teacher use for the standard error (rounded to two decimal places)?
10.00
12.00
1.71
2.06
2.06
Imagine that a study of memory and aging finds that younger participants correctly recall 55 percent of studied words, older participants correctly recall 42 percent of studied words, and the size of this effect is Cohen’s d = 0.32. According to Cohen’s conventions for interpreting d, this effect is:
large
so small as to be considered virtually no effect.
small
medium
small
Which of the following studies has the MOST statistical power?
a) A mean difference of 5, a two-tailed test, with sample size 50
b) A mean difference of 10, a one-tailed test, with sample size 100
c) A mean difference of 5, a one-tailed test, with sample size 100
d) A mean difference of 10, a one-tailed test, with sample size 50
D) NOPE. Forgot to look at sample size of 50…
CORRECT is B). Mean AND 1-tail test AND sample size allllllll increase POWER.
A researcher is studying whether older adults are more likely to fall if they are walking while talking than if they are only walking. They have 35 older adults walk while the researcher talks to them. They then have the same older adults walk with the researcher but with no conversation. In this study, the null hypothesis is that:
a) There is no difference between the number of falls when talking and not talking while walking or the number of falls is less while walking
b) There is no difference between the number of falls when talking and not talking while walking
c) There is a difference between the number of falls when talking and not talking while walking
d) The number of falls will be higher while talking than when not talking.
B) NOPE, NOT THE ANSWER.
A) the answer?
The null hypothesis typically states that there is no effect or no difference between the variables being studied. In this case, the researcher is examining whether there is a difference in the number of falls when older adults are walking while talking compared to when they are only walking. The null hypothesis assumes that there is no difference in the number of falls between the two conditions.
WEEK 7 QUIZ:
If we conduct the same study with different samples and get the same results each time, it is:
a) less likely that we will reject the null hypothesis
b) more likely we have an error in our results
c) more likely the results are accurate
d) less likely the results are accurate
C)
When we replicate findings, we become more confident in our results.
(Remember, we will get a Type I error 5% of the time, or every 1 out of 20 studies we run. If a finding can’t be replicated, it may well have been a Type I error).
It is known that the population mean on the math portion of the SAT is 527, with a standard deviation of 107. Assume that the average math SAT score for freshmen entering your college is 550, with a standard deviation of 110. What statistical analysis would you use to see if the freshman entering in the college score higher on the math SAT than the average population?
A) z test
B) single-sample t test
C) dependent-samples t test
D) standard deviation analysis
**A)
Since we know both the population mean and standard deviation, we can compute a z test**
WRONG B)
The reason for using a t-test instead of a z-test is that the population standard deviation is unknown in this case. While the population mean is given, the standard deviation is not specified for the entire population. Therefore, we use the sample data from the freshmen entering your college to estimate the population parameters and conduct the t-test.
The formula for the t-test is as follows:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
Mary is collecting data on the average age of onset of Alzheimer’s Disease. 140 people from a hospital participate in her study. If Mary wants to report the standard deviation of this variable for the population, what formula will she use?
C)
When we are estimating a standard deviation for a population from a sample, we correct for bias (underestimation) by dividing by N-1
Imagine that you are completing an attention task. Most of the time, you are paying attention and react quite quickly, but ever so often your mind wanders and you react quite slowly. What kind of distribution would you expect your data to look like?
a) normal
b) bimodal
c) positively skewed
d) negatively skewed
C)
In this case, there is a floor effect. You can’t be better than a zero response time, but you can have long response times (as might happen if your mind wanders). Thus, you would see a positive skew.
QQQQQQQ but 0.2 is on the chart???
Researchers examined the impact of candy on students’ test performance and found that candy significantly increased test performance. When they examined the effect size, they found that Cohen’s d was .02 Based on convention this is considered:
a) too small to be of interest
b) large
c) medium
d) small
A)
You are performing some research on mice. You have 36 mice and you would like to perform a single-sample t test to see if their maze scores are lower than the maze scores of the general mouse population. Which of the following is your research hypothesis?
B)
As sample size decreases, the shape of the t distribution:
a) more closely matches the z distribution.
b) is more accurate.
c) gets progressively wider.
d) gets progressively narrower.
C)
The t-distribution is used when the population standard deviation is unknown and is estimated using the sample data. As the sample size decreases, there is less information available to estimate the population parameters accurately. This increased uncertainty leads to wider tails in the t-distribution compared to the standard normal distribution (z-distribution), which has narrower tails. The t-distribution becomes closer to the standard normal distribution as the sample size increases, approaching the characteristics of the z-distribution.
The symbol used to designate the standard deviation when estimating from a sample is:
a) SD
b) (the standard deviatio symbol)
c) t
d) s
D)
Previously, we used the symbols SD for the standard deviation. However, that is only used when the purpose is a descriptive statistic. When we need to estimate the standard deviation based on our sample, we change the symbol to the little s.
See also the section on Estimating Population Standard Deviation from a Sample
With α = .05 and df = 8, the critical values for a two-tailed test are t = ± 2.306. Assuming that all other factors are held constant, if the df value were increased to df = 20, what would happen to the critical values for t?
a) They would decrease (move closer to zero).
b) They would stay the same.
c) They would increase (move farther from zero).
a)
TEACHER: One way to answer this question is to look at Table B.2. What happens when you increase the degrees of freedom?
OTHER: The other way is to understand some of the theory. If we increase our sample size, the t distribution gets narrower. That means our critical values will get closer to zero.
If the degrees of freedom (df) value were increased from df = 8 to df = 20, the critical values for t would decrease. Therefore, the correct answer is a) They would decrease (move closer to zero).
The t-distribution is influenced by the degrees of freedom. As the degrees of freedom increase, the t-distribution approaches the shape of the standard normal distribution (z-distribution). With a larger degrees of freedom value, the t-distribution becomes less spread out and closer to the standard normal distribution.
In this case, when the degrees of freedom increase from 8 to 20, the critical values for t would decrease, moving closer to zero. This means that the t-statistic would need to be more extreme in order to reject the null hypothesis, making it more challenging to obtain statistically significant results.
Imagine that you are completing a single-sample t-test with 20 participants. What is your degrees of freedom?
a) 20
b) 19
c) 21
d) 18
B)
The degrees of freedom for a single-sample t-test can be calculated by subtracting 1 from the sample size (n) because estimating the sample mean requires using one degree of freedom. In this case, with 20 participants, the degrees of freedom would be 20 - 1 = 19.
WEEK 7 QUIZ:
A researcher finds that chocolate helps cure cancer. The researcher publishes their data in an open source database. Another researcher downloads the data and analyzes the data based on the information posted by the original researcher, but doesn’t find the same results. When the researchers talk, it is clear the difference is due to the criteria the researchers used to determine outliers (one was more stringent than the other). This suggests that the original researcher:
A)did not publish enough information to support a reproducible analysis
B)engaged in p hacking
C)used too small a sample size to produce reliable results
D)failed to use a stringent enough alpha
A)
NOT D)
A study finds that 25 students coming from families with an economic income of less than $15,000 per year have a mean reading speed 100 words per minute, with a standard deviation of 50. The national average is a speeding read of 120 words per minute (the population standard deviation is unknown). Construct a 95% confidence interval for the sample.
[79.36 - 120.64]
[82.89 - 117.11]
[99.36 - 140.46]
[102.89 - 137.11]
A)
Confidence Interval = sample mean ± (critical value * standard error)
where the critical value is obtained from the t-distribution based on the desired confidence level and degrees of freedom (sample size minus 1), and the standard error is calculated as the sample standard deviation divided by the square root of the sample size.
Given:
Sample mean (x̄) = 100 words per minute
Sample standard deviation (s) = 50
Sample size (n) = 25
The degrees of freedom (df) for this sample is 25 - 1 = 24.
First, let’s calculate the standard error:
Standard Error (SE) = s / √n
SE = 50 / √25
SE = 10
Next, we need to determine the critical value for a 95% confidence interval with 24 degrees of freedom. Looking up the value in the t-distribution table or using a calculator, the critical value is approximately 2.064.
Now we can calculate the confidence interval:
Confidence Interval = x̄ ± (critical value * SE)
Confidence Interval = 100 ± (2.064 * 10)
Confidence Interval = 100 ± 20.64
Therefore, the 95% confidence interval for the sample mean reading speed is approximately [79.36 - 120.64].
Professor Milger would like to compare his classes SAT scores to the general population. This test has a mean of 500 and a standard deviation of 100. Professor Milgram’s class of 45 students scored 520 with a standard deviation of 80. Based on this information, what value should Professor Milgram use for the standard error (rounded to two decimal places)?
A) 14.91
B) 80
C) 100
D) 11.93
CORRECT A)
WRONG D)
Given:
Mean of the general population (μ) = 500
Standard deviation of the general population (σ /) = 100
Sample mean (x̄) = 520
Sample standard deviation (s) = 80
Sample size (n) = 45
The standard error (SE) can be calculated as follows:
wrong SE = s / √n
correct SE = σ / √n
Standard Error = population st.dev. / # of students of sample
wrong SE = 80 / √45
correct SE = 100 / √45
STANDARD ERROR ≈ 14.91
Therefore, Professor Milgram should use a standard error of approximately 14.91 when comparing his class’s SAT scores to the general population.
A researcher is interested in whether infants’ attention to their mothers’ voices increases in the first week of life. Let’s assume she tests four infants and finds the following values for infant attention (in seconds): 6, 6, 8, and 8 (thus, the average is 7).
She wishes to use the standard deviation to estimate the population standard deviation. Use the correct formula to calculate the standard deviation for the sample.
A) 1.33
B) 1
C) 4
D) 1.15
D)
To calculate the standard deviation for the sample, you can use the formula for the sample standard deviation:
s = √[(Σ(x - x̄)²) / (n - 1)]
where:
s = sample standard deviation
x = individual observation
x̄ = sample mean
n = sample size
Given the values of infant attention: 6, 6, 8, and 8, and the sample mean of 7, we can calculate the sample standard deviation.
First, calculate the squared differences from the sample mean for each observation:
(6 - 7)² = 1
(6 - 7)² = 1
(8 - 7)² = 1
(8 - 7)² = 1
Next, sum up these squared differences:
1 + 1 + 1 + 1 = 4
Now, divide the sum by (n - 1), where n is the sample size:
4 / (4 - 1) = 4 / 3 ≈ 1.33
Finally, take the square root of the result to obtain the sample standard deviation:
s ≈ √1.33 ≈ 1.15
The average age for licensed drivers in a county is 42.6. A county police officer was interested in whether the average age of drivers receiving speeding tickets differed from the average age of the driving population. She obtained a sample of N = 16 drivers with speeding tickets. The average age for this sample was M = 34.4 with a standard deviation of 12. What is the effect size for this data?
A) -.80
B) -0.68
C) 2.73
d) 0.34
B)
A single-sample t test is conducted on a sample of 23 people who were selected from a large population estimated at 2500 people. The critical cutoff for a two-tailed test at a p level of 0.01 would be:
A) -2.069 and 2.069
B) -1.717 and 1.717
C) -2.074 and 2.074
D) -2.819 and 2.819
D)
To determine the critical cutoff for a two-tailed t-test at a p level of 0.01, we need to consider the degrees of freedom (df) and consult the t-distribution table or use a statistical calculator.
In this case, a single-sample t-test is conducted on a sample of 23 people. For a single-sample t-test, the degrees of freedom are equal to the sample size minus 1: df = n - 1.
Given that the sample size (n) is 23, the degrees of freedom would be 23 - 1 = 22.
For a two-tailed test at a p level of 0.01, we need to split the significance level in half because we have two tails. Each tail would have an area of 0.01 / 2 = 0.005.
Using the degrees of freedom (df = 22) and the tail area (0.005), we can find the critical t-value from the t-distribution table or a statistical calculator.
Looking up the critical t-value for df = 22 and a tail area of 0.005, we find it to be approximately ±2.807.
Therefore, the critical cutoff for a two-tailed t-test at a p level of 0.01 would be ±2.807.
A researcher is studying whether socio-economic status affects memory. She takes a sample of 83 participants classified as low SES and gives them the a standardized memory test. She knows the population mean is 34.56 items. The mean memory score for her participants is 33.41 with a standard deviation of 4.36. What is the t-statistic (round to two decimal places)?
A) -0.25
B) -0.26
C) -2.40
D) -2.38
C)
To calculate the t-statistic, we can use the formula:
t = (x̄ - μ) / (s / √n)
where:
t = t-statistic
x̄ = sample mean
μ = population mean
s = sample standard deviation
n = sample size
Given:
Sample mean (x̄) = 33.41
Population mean (μ) = 34.56
Sample standard deviation (s) = 4.36
Sample size (n) = 83
Substituting these values into the formula, we can calculate the t-statistic:
t = (33.41 - 34.56) / (4.36 / √83)
t = (-1.15) / (4.36 / √83)
t = (-1.15) / (4.36 / 9.11)
t = (-1.15) / 0.477
t ≈ -2.41
Therefore, the t-statistic for this study is approximately -2.41
In one statistics course, students reported studying an average of 10.82 hours a week, with a standard deviation of 3.69. Treating this class as the population, what is the percentile for a student in the class who studies 8 hours a week? (Round z score to two decimal places.)
A) 33.72
B) 22.36
C) 53.72
D) 72.36
B)
o determine the percentile for a student who studies 8 hours a week, we need to calculate the z-score and then find the corresponding percentile from the standard normal distribution.
The z-score is calculated using the formula:
z = (x - μ) / σ
where:
z = z-score
x = value we want to find the percentile for (8 hours)
μ = population mean (10.82 hours)
σ = population standard deviation (3.69)
Substituting the given values into the formula, we can calculate the z-score:
z = (8 - 10.82) / 3.69
z = -2.82 / 3.69
z ≈ -0.764
To find the percentile corresponding to this z-score, we can use a standard normal distribution table or a statistical calculator. The percentile associated with a z-score of -0.764 is approximately 22.26%.
Therefore, a student who studies 8 hours a week would be at the 22.26th percentile in the class
The average salary for all 30 employees in a branch of a tech company is $46,789 with a standard deviation of $24,893. The population, all the employees in all of the tech company branches, earned an average salary of $51,256, with unknown variability. Does the average salary of the 30 employees differ from that of the employees in ALL of the branches of the company? What statistical analysis is used to answer this question?
A) single-sample t test
B) standard deviation analysis
C) dependent-samples t test
D) z test
A)
To answer the question of whether the average salary of the 30 employees in a branch differs from that of the employees in all of the branches of the company, we would need to compare the sample mean (from the branch) to the population mean (from all branches).
Given that we have information about the sample mean ($46,789), the sample standard deviation ($24,893), and the population mean ($51,256), we can use a statistical analysis to test the difference between the sample mean and the population mean.
The appropriate statistical analysis to answer this question is a single-sample t-test (option A). The single-sample t-test is used when comparing the mean of a sample to a known or hypothesized population mean.
In this case, we can set up the null hypothesis (H0) as: “The average salary of the 30 employees in the branch is equal to the average salary of the employees in all of the branches of the company.” The alternative hypothesis (Ha) would be: “The average salary of the 30 employees in the branch is different from the average salary of the employees in all of the branches of the company.”
By performing a single-sample t-test, we can calculate the t-statistic using the sample mean, sample standard deviation, population mean, and the sample size (30). We can then compare the t-statistic to the critical value(s) from the t-distribution to determine if we reject or fail to reject the null hypothesis.
Therefore, the correct answer is A) single-sample t test.
A researcher determines that their critical values for the single-sample t-test are -2.086 and 2.086. Which of the following t statistics would lead you to reject the null hypothesis?
A) 1.756
B) 1.943
C) 2.184
D) both a) and b)
C)
WEEK 8 QUIZ:
WEEK 8 QUIZ QUESTIONS:
Dependent sampling generally results in a more powerful statistical test than independent sampling because:
a) the dependent procedure generally has a larger N.
b) dependent procedures have higher acceptable levels of alpha.
c) dependent procedures reduce the variability in the sampling distribution.
d) all of the above are correct
D) —NOPE
C) CORRECT –In a repeated-sampling procedure, every participant gets to participate in each level of the independent variable. That means there will be no differences in things like IQ, gender, or fatigue between the groups. That reduces variability.
a) The dependent procedure generally has a larger N: Dependent sampling often involves repeated measurements or pairs of related observations, which can increase the effective sample size and provide more information for the statistical analysis. This larger sample size can lead to increased statistical power.
b) Dependent procedures have higher acceptable levels of alpha: In some cases, when dependent sampling is used, the acceptable level of significance (alpha) can be adjusted to account for the dependence structure. This adjustment allows for a more lenient threshold for rejecting the null hypothesis, which can increase the power of the test.
c) Dependent procedures reduce the variability in the sampling distribution: When observations are dependent, there is often a correlation or relationship between them. This dependence can reduce the variability in the sampling distribution, making it easier to detect significant differences between groups or conditions. Reduced variability can increase the power of the statistical test.
Therefore, all of the options (a), (b), and (c) are correct explanations for why dependent sampling generally results in a more powerful statistical test than independent sampling.
The fact that a research participant encounters the dependent variable twice in a within-groups design means that we have to be concerned about:
a) compensating participants
b) order effects
c) gender differences
d) using statistics
B)
In a within-groups design, participants encounter the dependent variable multiple times under different conditions or treatments. This repeated exposure to the dependent variable introduces the possibility of order effects, which refers to the influence that the order or sequence of the conditions may have on participants’ responses.
Order effects can manifest in different forms. One common type is the practice effect, where participants may improve their performance or become more familiar with the task over time, leading to biased results. Conversely, fatigue effects can occur if participants’ performance deteriorates as they go through the different conditions.
To mitigate order effects, researchers often implement counterbalancing techniques. Counterbalancing involves systematically varying the order of conditions across participants, such as using a Latin square or randomizing the presentation order. By doing so, researchers can control for the potential influence of order effects on the dependent variable.
Therefore, the concern that arises in a within-groups design due to encountering the dependent variable twice is primarily related to order effects (option b). Compensating participants (option a), gender differences (option c), and using statistics (option d) are not direct concerns specifically associated with encountering the dependent variable twice in a within-groups design
A researcher asks participants to drink caffeine and subsequently measures their aggression. Two weeks later, the participants return. This time they receive a placebo drink. What type of test is most appropriate for this study?
a) a paired-samples t test
b) a z test
c) an independent-samples t test
d) a single-sample t test
A)
In this study, participants are measured twice under two different conditions: once after consuming caffeine and once after consuming a placebo. Since the same participants are measured under both conditions, a paired-samples t test would be the most appropriate statistical test.
The paired-samples t test, also known as a dependent-samples t test or a within-subjects t test, is used when the same participants are measured under two different conditions, treatments, or time points. It is used to determine whether there is a significant difference in the means of the paired observations.
Why not use the other tests?
A z test is not suitable because it is typically used when working with large sample sizes and known population parameters. An independent-samples t test compares the means of two independent groups, which is not applicable in this scenario. A single-sample t test compares the mean of a single group to a known population mean, which does not align with the study design described.
According to the null hypothesis, the mean of the comparison distribution for a paired-samples t test is:
a) sometimes 1
b) sometimes 0
c) always 0
d) always 1
C)
In a paired-samples t test, the null hypothesis assumes that there is no difference between the paired observations or conditions. Specifically, it assumes that the mean difference between the paired observations is zero. Therefore, the mean of the comparison distribution, which represents the distribution of sample mean differences under the null hypothesis, is always 0.
The paired-samples t test compares the mean difference between paired observations to the mean difference expected under the null hypothesis (which is 0). If the observed mean difference significantly deviates from 0, it provides evidence to reject the null hypothesis and conclude that there is a statistically significant difference between the paired conditions
A paired-samples t test is also known as a(n):
a) independent-sample t test
b) dependent-sample t-test
c) single-sample t test
d) confidence interval
B)
Dr. Singh has 40 participants in his paired-samples t test. What is the degrees of freedom?
a) 37
b) 39
c) 38
d) 40
B)
Rachel is doing a study on the consequences of social exclusion. She asks people to put their hand in cold water and rate their pain on a scale of 1 to 10 after either being socially included or excluded. She finds that people experience more pain after social exclusion. If Rachel’s conclusion is an error, she made a THIS ERROR
a) Type I
b) Type II
c) Type B
d) Type A
A)
In statistical hypothesis testing, a Type I error occurs when the researcher incorrectly rejects the null hypothesis when it is actually true. In other words, it is a false positive result where the researcher concludes there is a significant effect or difference when there is none in reality
Which of the following is the correct comparison distribution for a paired-samples t test?
a) A distribution of means
b) A distribution of mean differences
c) A distribution of differences between means
d) A distribution of scores
B)
In a paired-samples t test, the analysis focuses on the differences between paired observations or conditions within the same participants. The goal is to determine whether there is a significant difference between the mean differences observed in the sample and the mean difference expected under the null hypothesis.
To construct the comparison distribution, the mean difference is calculated for each pair of observations. The distribution of these mean differences is then used to assess the significance of the observed mean difference.
Counterbalancing minimizes order effects by:
a) including a lot more research participants in the study
b) converting the within-subject design to a between-subject design
c) randomly assigning participants to conditions
d) varying the order of presentation of different levels of the IV from one participant to the next
b) nope
D) , CORRECT
By varying the order, we can reduce order effects caused by factors such as fatigue. See the section on Next Steps in Chapter 10
Carlos is doing a study on depression. He takes a sample of 30 college students diagnosed with depression from the Langara population.
When Carlos calculates the standard deviation for his sample, what will be the denominator or his calculation?
29
WEEK 9 SELF-ASSESSMENT QUIZ:
An independent-samples t test is used with which type of research design?
a) A within-groups design
b) A single-sample design
c) A between-groups design
d) A paired-samples design
C)
A between-groups design, also known as an independent groups design, is a research design in which participants are assigned to different groups or conditions. Each group receives a different treatment or condition, and the groups are independent of each other. The purpose of a between-groups design is to compare the differences between the groups to determine the effect of the independent variable on the dependent variable.
In the context of an independent-samples t-test, a between-groups design would involve comparing the means of two separate groups to determine if there is a significant difference between them. The t-test is used to analyze the means of two independent samples and determine whether the difference between them is statistically significant.
An independent-samples t test is used with which type of research design?
a) A within-groups design
b) A single-sample design
c) A between-groups design
d) A paired-samples design
C)
A between-groups design, also known as an independent groups design, is a research design in which participants are assigned to different groups or conditions. Each group receives a different treatment or condition, and the groups are independent of each other. The purpose of a between-groups design is to compare the differences between the groups to determine the effect of the independent variable on the dependent variable.
In the context of an independent-samples t-test, a between-groups design would involve comparing the means of two separate groups to determine if there is a significant difference between them. The t-test is used to analyze the means of two independent samples and determine whether the difference between them is statistically significant.
Dr. Levine is doing a study on the effects of meditation on well-being. He recruits 10 participants whom rate their mental health a week after meditating for 10 minutes every day. They then rate their mental health a week after watching TV for 10 minutes every day. What type of test should Dr. Levine employ for this design?
a) A paired-samples t test
b) A z test
c) An independent samples t test
d) A single-sample t test
A)
Dr. Levine’s study design involves comparing the ratings of participants before and after two different conditions (meditation and watching TV). Since the same participants are being measured under both conditions, this is a within-groups design, also known as a paired-samples design or repeated measures design.
When using an independent-samples t test, we have to create a:
a) distribution of differences between raw scores
b) distribution of mean differences
c) difference score for each participant
d) distribution of differences between means
D)
In an independent-samples t test, we compare the means of two independent groups or conditions. To conduct the test, we calculate the difference between the means of the two groups and examine the distribution of these differences. This distribution represents the variability between the means of the two groups and is used to determine the statistical significance of the difference.
PROF: Oh… wording. In this case we are using a distribution of differences between means. We are looking at one mean minus another mean. This is different from our distribution of mean differences, where we are looking at average differences between pairs.
Which of the following statements is a correctly worded null hypothesis for an independent-samples t test?
a) On average, women categorize the same percentage of cartoons as being funny as men do.
b) On average, women categorize a different percentage of cartoons as being funny as men do.
c) On average, women categorize a larger percentage of cartoons as being funny as men do.
d) On average, women categorize a smaller percentage of cartoons as being funny as men do.
A)
The weighted average of the two estimates of variance (one from each sample) that are calculated when conducting an independent-samples t test is referred to as:
a) degrees of freedom
b) pooled variance
c) standard error
d) the confidence interval
B)
Since we are working with two samples, an estimate of spread based on two samples is likely to be more accurate than an estimate of spread based on a single sample. This is why we used the pooled variance.
See also Chapter 10 The Six Steps of the Independent-Samples t Test.
You are conducting an independent-samples t test with 18 participants in each of two groups. What is the total degrees of freedom for this problem?
a) 17
b) 16
c) 35
d) 34
D)
It’s N-1 for both groups.
So 18-1 and 18-1 equals 17 + 17 = 34
If a t score is calculated to be –.03 and our critical values are –2.365 and 2.365, what decision do we make about our research study?
a) Accept the null hypothesis
b) Reject the null hypothesis
c) Accept the research hypothesis
d) Fail to reject the null hypothesis
D)
Since -2.365 < -0.03 < 2.365
the t-score is within the range of the critical values, FAIL TO REJECT THE NULL HYPOTHESIS
The 95% confidence interval for Mx – My does not include 0. If the H0 that mx – my = 0 were now being tested,
a) the difference between Mx – My would not be significant at the .05 level.
b) the difference between Mx – My would be significant at the .05 level.
c) the difference between Mx – My would be significant at the .025 level.
d) Nothing can be said about the significance of the difference at this point.
B)
When the confidence interval does not include 0, it indicates that the observed difference between the means (Mx - My) is statistically significant at the specified level of significance (in this case, 0.05). This means that we can reject the null hypothesis and conclude that there is a significant difference between the two groups or conditions being compared.
For which of the following dependent variables would you be unable to perform an independent-samples t test?
a) Temperature, measured in Celsius
b) Reaction time, measured in ms
c) Eye colour, measured as blue, green, brown, or hazel
d) Agreement, measured on a Likert scale
C)
When using _, the researcher is interested in existing evidence about a particular phenomenon.
a) power analysis
b) confidence intervals
c) Bayesian analysis
d) hypothesis testing
C)
Baysesian analyses use our beliefs to adjust the analysis. In this way, the analysis is much more akin to the type of decision-making we make every day. See also the Data Ethics box in Chapter 11: Beyond Hypothesis Testing.
QUIZ WEEK 9:
Ron Weasley thinks that students from Slytherin (N = 40) is receiving more cupcakes than Gryffindor (N = 38). He decides to perform an independent samples t-test to explore the claim. He finds the average number of cupcakes per student in Slytherin is 4 and for Gryffindor is 2.6. He also knows that the pooled variance for his study (
) is 11.50. He needs to determine his measure of spread. In this study,
is:
a) 0.58
b) 0.29
c) 0.77
d) 0.30
D)
A researcher is interested in the effect caffeine has on driving. She asks people to come to the lab and do a simulated driving test after drinking 70 mg of caffeine or after having a placebo drink. What type of research design has the researcher employed?
a) between-groups
b) operational
c) correlational
d) within-groups
A)
In a between-groups design, different groups of participants are assigned to different conditions or treatments. In this case, the participants are divided into two groups: one group receives 70 mg of caffeine, while the other group receives a placebo drink. Each group represents a different condition or treatment.
The average salary for all 30 employees in a branch of a tech company is $46,789 with a standard deviation of $24,893. The population, all the employees in all of the tech company branches, earned an average salary of $51,256 with a standard deviation of $15,389. Does the average salary of the 30 employees differ from that of the employees in ALL of the branches of the company? What statistical analysis is used to answer this question?
a) z test
b) single-sample t test
c) independent-samples t-test
d) paired-samples t-test
B)
To answer the question of whether the average salary of the 30 employees in the branch differs from that of the employees in all of the branches of the company, we need to compare the sample mean to the population mean. Since we are comparing one sample to a known population, the appropriate statistical analysis to use in this scenario is a single-sample t-test.
A single-sample t-test is used to determine whether the mean of a sample differs significantly from a known population mean when the population standard deviation is unknown or not available. In this case, we have the sample mean ($46,789) and standard deviation ($24,893) for the 30 employees in the branch, as well as the population mean ($51,256) and standard deviation ($15,389) for all the employees in all of the tech company branches.
If the standard error for a group was 2, and the mean of the group was 6, for which values would the standard error bars begin and end on a bar graph?
a) 4 and 8
b) 2 and 4
c)-2 and 2
d)6 and 8
A)
The standard error bars typically extend one standard error above and below the mean. Since the standard error is 2, we can calculate the values by adding and subtracting 2 from the mean:
Upper limit: 6 + 2 = 8
Lower limit: 6 - 2 = 4
Therefore, on the bar graph, the standard error bars would begin at 4 and end at 8.
A researcher would like to explore whether a cognitive-behavioural therapy program improves binge eating. She has forty participants in her study. She randomly assigns 20 participants to participate in her program for two weeks. At the end of the two weeks, she measures the the amount of binge eating in her participants. She finds control group scopes 8 on her scale and her experimental group scores 6. What would be the mean of the comparison distribution used in the statistical analysis for this study?
a) -2
b) 2
c) 0
d) 1
A)
Mean of the comparison distribution = Experimental group mean - Control group mean
Mean of the comparison distribution = 6 - 8
Mean of the comparison distribution = -2
A researcher is studying the Bystander Effect. Since there is extensive research on this study, she attempts to use previous knowledge of the findings to help with her statistical analysis. She is likely conducting a:
a) Nonparametric test
b) preregistration analysis
c) Bayesian analysis
d) Gaussian analysis
A)
Nonparametric tests are statistical analyses that do not make specific assumptions about the underlying distribution of the data. They are often used when the data do not meet the assumptions of parametric tests, such as normality or homogeneity of variances. Nonparametric tests are also useful when the sample size is small or when the data are measured on ordinal or nominal scales.
In this case, the researcher is using previous knowledge of the findings to inform her statistical analysis. By leveraging existing research on the Bystander Effect, she is likely using nonparametric tests that are commonly applied in this area of study. These tests allow her to analyze the data without relying on specific assumptions about the distribution of the data.
Assume the following for an independent-samples t test:
Number of participants in group 1: 32
Number of participants in group 2: 48
Mean of group 1: 68
Mean of group 2: 76
s_difference = 5
Construct a 90% confidence interval around the data.
[-16.355, 0.355]
[-16.32, -0.32]
[-17.95, 1.95]
[-18.05, 2.01]
[-16.355, 0.355]
CI = (X1 - X2) ± t * SE
Where:
X1 and X2 are the means of group 1 and group 2, respectively.
t is the critical value from the t-distribution for the desired confidence level and degrees of freedom.
SE is the standard error of the difference between the means.
First, let’s calculate the standard error (SE) of the difference between the means:
SE = sqrt((s1^2 / n1) + (s2^2 / n2))
Where:
s1 and s2 are the standard deviations of group 1 and group 2, respectively.
n1 and n2 are the sample sizes of group 1 and group 2, respectively.
In this case, the standard error of the difference between the means (SE) is given as 5.
To construct the confidence interval, we need the critical value from the t-distribution. With 30 degrees of freedom (32 + 48 - 2), a 90% confidence level corresponds to a critical value of approximately 1.697 (obtained from a t-distribution table or calculator).
Now, let’s calculate the confidence interval:
CI = (X1 - X2) ± t * SE
= (68 - 76) ± 1.697 * 5
= -8 ± 1.697 * 5
= -8 ± 8.485
= (-16.485, 0.485)
Therefore, the 90% confidence interval for the difference in means between the two groups is approximately (-16.485, 0.485).
Among the given options, the closest interval is [-16.355, 0.355].
