Exam III Review Flashcards
A binomial experiment has the following properties…
A fixed number (n) of trials.
The result of each trial falls into one of two categories.
* Usually denoted “success” or “failure”
Each trial is independent.
The probability of success (p) is the same for every trial.
Binomial distributions are
Symmetric when _______.
p = 0.5
Binomial distributions are
Positively skewed when _______.
p < 0.5
Binomial distributions are
Negatively skewed when _______.
p > 0.5
Binomial standard error _______.
Increases with n
Increases as p and (1 – pi)
approach 0.5
Binomial mean _______.
increases with n and with pi
A binomial variable X is just _______.
the sum of n independent and
identical Bernoulli variables Y
T or F
The sampling distribution of the proportion is not a binomial distribution.
T, It’s a scaled down version
In which of the following cases will the binomial distribution be perfectly symmetric?
A. pi = 0.1 and n = 100
B. pi = 0.95 and n = 100
C. pi = 0.95 and n = 20
D. pi = 0.1 and n = 20
E. pi = 0.5 and n = 20
E. pi = 0.5 and n = 20
T or F
In poll for an election involving two candidates, the margin of error for the difference between the candidates’ proportions is the same as the margin of error for the leading candidate.
F
Which of the following statements about the margin of error is TRUE?
T or F
In a political poll, the reported margin of error typically corresponds to the 95% confidence interval.
T
Which of the following statements about the margin of error is TRUE?
T or F
For a given sample size, the margin of error for a single proportion is smaller when the observed proportion is 0.5 than when it is 0.8.
F
Which of the following statements about the margin of error is TRUE?
T or F
To reduce the margin of error for one proportion by a factor of 2, you need to double the sample size.
F
Imagine that you are comparing the means from two samples, and that one of the samples is larger than the other. Which of the following statements about an equal-variance two-sample t test is FALSE?
T or F
The degrees of freedom for the test equal the sum of the two sample sizes minus 2.
T
Imagine that you are comparing the means from two samples, and that one of the samples is larger than the other. Which of the following statements about an equal-variance two-sample t test is FALSE?
T or F
In the calculation of the pooled variance, the larger sample gets more weight than the smaller sample.
Correct!
T
Imagine that you are comparing the means from two samples, and that one of the samples is larger than the other. Which of the following statements about an equal-variance two-sample t test is FALSE?
T or F
For a two-tailed test with alpha = .05, the critical value of t is +/– 1.960.
F
Imagine that you are comparing the means from two samples, and that one of the samples is larger than the other. Which of the following statements about an equal-variance two-sample t test is FALSE?
T or F
If the p-value for a two-tailed test is less than .05, the 95% confidence interval for the difference between the means will NOT include zero.
T
Holding the sample size constant, at what value of pi (the population proportion) will the standard deviation of the sampling distribution of the proportion be largest?
A. 0.25
B. 1
C. 0.5
D. 0
E. The standard deviation does not depend on pi.
C. 0.5
Which of the following statements about Cohen’s d is FALSE?
It is an effect size measure for the difference between the means of two samples.
Because n is in the denominator, Cohen’s d is very sensitive to sample size.
It has the same sign as the calculated t statistic.
It is equal to the difference between two means, divided by the pooled standard deviation.
Because n is in the denominator, Cohen’s d is very sensitive to sample size.
A choice experiment has 2 conditions (A and B) and three choice options (1, 2, and 3). There are 150 participants, 72 in condition A and 78 in condition B. Across both conditions, 88 participants choose option 1, 46 participants choose option 2, and 16 participants choose option 3. For a chi-square test of independence, what it the expected number of participants in condition A that choose option 3?
7.68
25.00
24.00
8.00
7.68
In a two-tailed test of whether two proportions from independent samples are equal, the p-value is .15. What is the correct interpretation of this p-value?
Assuming the null hypothesis that the two proportions are equal is true, the chance of observing a difference as extreme as or more extreme than the one observed, in the same direction, is .15.
Assuming the null hypothesis that the two proportions are equal is true, the chance of observing a difference as extreme as or more extreme than the one observed, in either direction, is .15.
Based on the observed difference between the proportions, there is a .15 chance that the alternative hypothesis that the proportions are different is true.
Based on the observed difference between the proportions, there is a .15 chance that the null hypothesis that the two proportions are equal is true.
Assuming the null hypothesis that the two proportions are equal is true, the chance of observing a difference as extreme as or more extreme than the one observed, in either direction, is .15.
When testing whether an observed proportion is significantly greater than 0.5, which of the following tests yields the most accurate results?
A z test with the continuity correction
A binomial test
A z test without the continuity correction
A single-sample t test
A binomial test
Which of the following statements about chi-square tests is FALSE?
The p-value for a chi-square test comes only from the right (upper) tail of the distribution.
If the observed count in a cell is less than the expected count, that cell’s contribution to the overall chi-square is negative.
When comparing two proportions, a two-tailed z test for comparing the proportions gives the same result as a chi-square test for a contingency table with two rows and two columns.
For a “goodness of fit” chi-square test involving one variable, degrees of freedom equal the number of categories minus 1.
If the observed count in a cell is less than the expected count, that cell’s contribution to the overall chi-square is negative.
The standard error for a one-proportion test depends on _______.
the hypothesized population proportion
Cutting the margin of error in half requires _______ the sample size.
quadrupling
Cohen’s D , or standardized mean difference, is one of the most common ways to measure _______.
effect size
An effect size is _______.
how large an effect is,or the measure of the strength of the relationship between two variables. For example, medication A has a larger effect than medication B.
The margins of error for subgroups (e.g., college-educated women)
are _______ than for the whole.
larger
The margin of error for the difference between candidates is _______ the margin of error for one candidate.
twice
For a chi-square test, the mean of the distribution is equal to _______.
df
As df increases, the distribution for a chi-square test _______.
becomes more normal
Rule of Five
If any of the expected cell frequencies is less than five, note this fact and interpret the results with caution.
Fisher’s exact test
A statistical significance test used in the analysis of contingency tables. Although in practice it is employed when sample sizes are small, it is valid for all sample sizes
Why do we use the chi-square test?
Comparing more than two proportions
For example, in studies with three or more different conditions
Are the proportions in the different conditions all the same, or are some of them different?
In other cases, there are more than two columns and more than two rows.
Is the frequency distribution of one variable related to the frequency distribution of another variable, or are the two variables independent?
For example, can you predict a person’s political affiliation if you know the person’s race or religion?
What is the relationship between chi-square and z for comparing 2 proportions?
The tests yield exactly the same result for comparing two proportions.
Cohen’s D
Calculate by taking the difference between the two means and dividing by the pooled sd. This reports size of mean difference by comparing it to the data’s variability.
A large Cohen’s d indicates _______.
the mean difference is large compared to the variability
0.2 small
0.5 med
0.8 large
DF for Correlation
n - 2
Fisher transformation
r to z
R squared
Proportion of the variation in y that is explained by x
What does the t mean for tests of intercept and slope?
How far each b is from zero in units of its standard error
Unless the slope is 0, SSe _ SSy
<
R squared is the _______.
proportional reduction in the sum of squared errors
Why use adjusted R squared?
R squared alone is a biased estimate of the true proportion of variance explained in the population.
Adjusted R squared is always _______ than R squared.
smaller, better at describing variance
Residual standard error
Standard deviation around the regression line rather than the mean, y-bar
Prediction interval
Represents a range of values that are likely to contain the true value of some response variable for a single new observation based on values of predictor variable(s)
Multiple regression is just like simple linear regression,
but with _______.
more predictor variables
Multicollinearity
Correlations among predictor variables
Multicollinearity can _______.
make interpretation of the multiple regression difficult
Significance tests asses _______.
whether a predictor variable explains additional variation in the dependent variable, once the other predictors have been taken into account. (over and above)
What are the df for the individual predictors t-test?
n – k – 1, where k is the number of predictors.
F test indicates _______.
whether all of the predictors taken together do a good job of predicting the dependent variable
R squared ____estimates the proportional reduction in variance.
over
