Statistics Subject Review Flashcards
What method might be used to avoid bias in a clinical study?
a. Exclude patients from the study if the investigator would know their status.
b. Make interviewers aware of patients’ study status to tailor questions appropriately.
c. Predetermine assignments of patients to study cohorts.
d. Select patients randomly using rigorous criteria to avoid confounding results
d. Select patients randomly using rigorous criteria to avoid confounding results
Two events, A and B, are independent. The probability of A is 0.2, the probability of B is 0.3. What is the probability of A and B?
a. 0.06
b. 0.23
c. 0.32
d. 0.50
a. 0.06
The events are independent, so the probability of both events is the product of the individual probabilities.
0.2 × 0.3 = 0.06
Case:
A researcher wants to study the effects of a new drug on people with heart disease. They acquire a random sample of local volunteers with heart disease using a random number generator. For the first trial study, the researcher randomly assigns each participant to the control group or the treatment group—by a coin toss—and gives each a placebo or the trial drug, respectively, then monitors and evaluates the results.
Question:
To what population can the results of this study be applied?
a. All local people with heart disease
b. All local people with or without heart disease
c. All people with heart disease
d. All people with or without heart disease
a. All local people with heart disease
What are the first quartile, second quartile, and third quartile of the following data set?
9, 5, 3, 7, 14, 5, 12
a. 3, 9, 14
b. 5, 7, 12
c. 9, 12, 14
d. 12, 5, 7
b. 5, 7, 12
The table below shows the street crime data of 5 cities. The xi column shows the number of cell phones stolen last year in the City i. The yi column shows the number of vehicles stolen last year in the City i.
What is the regression equation for this data?
a. ˆy = 0.6x + 30.2
b. ˆy = 0.8x + 22.4
c. ˆy = 0.5x + 20.7
d. ˆy = 0.3x + 10.8
a. ˆy = 0.6x + 30.2
When is the point estimator A a more efficient estimator for a given parameter than the point estimator B?
a. Both A and B have equal variance, but A is easier for a computer to calculate.
b. Point estimator A requires a smaller sample size to estimate B than calculating B requires.
c. The variance of A is always greater than the variance of B.
d. The variance of A is always less than the variance of B.
d. The variance of A is always less than the variance of B.
Case:
The Poisson Distribution is used to describe the probability that a certain number of successes will occur in a given amount of time. The distribution has only one parameter, which measures the average rate of successful events (known as lambda ‘lambda’ typically), and gives the probability of seeing ‘x’ successes.
The probability function of the Poisson distribution is defined as:
(the picture)
and is interpreted as “the probability of seeing exactly x number of successes”.
You are responsible for managing the emergency department of a small urgent care facility and are currently assigned to oversee the night shift. You have determined that 1 nurse needs to be on staff for every 3 patients. You currently have only 1 nurse on staff for this shift.
Because patients enter the ED randomly, you have determined that the Poisson distribution will describe the number of patients you are likely to receive. Based on past data, you realize that patients enter the ED at an average rate of 2 per shift.
Question:
What is the probability that you will exceed the number of patients that you can care for?
a. 0.14
b. 0.18
c. 0.86
d. You will never have more than 2 patients.
a. 0.14
Considering a test of the null and alternative hypotheses, what statement is correct?
a. Both the null and alternative hypotheses must be true.
b. Exactly one hypothesis must be true.
c. It is possible for both the null and alternative hypotheses to be true.
d. It is possible for neither the null or alternative hypotheses to be true.
b. Exactly one hypothesis must be true.
Case:
A survey population was asked, “How many minutes do you need to get ready for a party?” The responses of 15 men and 15 women have been recorded randomly.
Question:
What relationship exists among the survey responses?
a. Men take 1 minute 30 seconds longer than women on average.
b. Men take 1 minute 18 seconds longer than women on average.
c. Women take 1 minute 30 seconds longer than men on average.
d. Women take 1 minute 18 seconds longer than men on average.
d. Women take 1 minute 18 seconds longer than men on average.
A machine produces items. Each item is independently produced and has a 5% chance of failing quality control checks. If 1000 items are produced during a shift, what is the expected number of good items?
a. 7
b. 50
c. 950
d. 1000
c. 950
Case:
1000 students took an exam. The results are normally distributed with mean 72 and standard deviation 4.
The following values are from a table of the normal cumulative distribution function.
Question:
What is the probability that a student scored higher than a 68 on the exam?
a. 15.87%
b. 50%
c. 84.13%
d. 99.87%
c. 84.13%
Case:
When astronauts have recently returned to Earth, their bodies have a harder time regulating their blood pressure during position changes due to a temporary suppression of their otolith system. Two days after returning from space, astronauts on average have a standing pulse pressure value of 41.7 mm Hg, with a standard deviation of 16.8 mm Hg.
Question:
If we take a random sample of 36 astronauts, what is the probability the mean standing pulse pressure will be greater than 43.0 mm Hg?
a. -0.46
b. 0.32
c. 0.46
d. 0.68
b. 0.32
What is the most accurate description of the null hypothesis?
a. Mean differences are observable but attributed to error and sampling.
b. Mean differences observed between populations are significant, true, and valid.
c. There are differences between populations, but they cannot be explained.
d. There are no significant observable differences between populations.
d. There are no significant observable differences between populations.
Two events, A and B, are mutually exclusive. The probability of event A is
1/7. The probability of event B is 1/5. What is the probability of event A or event B?
a. 1/35
b.1/12
c. 11/35
d. 12/35
d. 12/35
A group of 5 people participated in a psychological study performed to assess the relationship between the person’s age and the total number of active hours in a day. Records were taken from each of these people and the results obtained are shown in the table below:
Assuming that the above data represents the populations, what is the correlation coefficient between the age and physical activity hours per day for this sample?
a. -0.9948
b. -0.4974
c. 0.4974
d. 0.9948
a. -0.9948
The linear regression equation has the following general form (without error):
ˆy = b1x + b0
Which variable is a slope and what does it describe?
a. b0 represents the point where the graph crosses the x-axis.
b. b1 represents the point where the graph crosses the x-axis.
c. b0 represents the rate of change in ˆy for one unit increase in x.
d. b1 represents the rate of change of ˆy for one unit increase in x.
d. b1 represents the rate of change of ˆy for one unit increase in x.
How will two confidence intervals (90% and 98%) constructed from the same data compare?
a. The 98% confidence interval is better than the 90% confidence interval.
b. The 98% confidence interval is less likely to include error.
c. The 98% confidence interval will be narrower than the 90% confidence interval.
d. The 98% confidence interval will be wider than the 90% confidence interval.
d. The 98% confidence interval will be wider than the 90% confidence interval.
A Bernoulli random variable consists of a single experiment that can give a yes (1) or a no (0). The probability of a yes is
p, and the probability of a no is (1 − p). You conduct an experiment in which the probability of a 1 is 70%. The probability of a 0 is 30%. What is the expected value of this experiment?
a. 0
b. 0.3
c. 0.7
d. 1
c. 0.7
Why might a two-tailed test be used to test a hypothesis instead of a one-tailed test?
a. It can be performed on smaller sample sizes.
b. It creates no expectation about the direction of effect.
c. It is more likely to return a significant result.
d. It is more powerful than the one-tailed test.
b. It creates no expectation about the direction of effect.
The scatter plot shows the relation between two variables. Which of the following is true? Refer to the image.
a. The relation is weak.
b. The slope is positive.
c. The relation is strong and the slope is zero.
d. The relation is strong and the slope is positive.
c. The relation is strong and the slope is zero.
The table below shows the results of 2 class sections that took a statistics exam and received either an A or B.
What is true about the students who received an A and are in Section 1?
a. Both are dependent because P(from section 1|A grade) = P(from section 1).
b. Both are independent because P(from section 1|A grade) = P(from section 1).
c. Both are dependent because P(from section 1|A grade) ≠ P(from section 1).
d. Both are independent because P(from section 1|A grade) ≠ P(from section 1).
c. Both are dependent because P(from section 1|A grade) ≠ P(from section 1).
The selection process for the inter-school football tournament has been conducted. A physician was there to assess the physical condition of every student. The physician found that a few of the students are flat-footed, a few have a knee-knock issue, and a few have both conditions. These problems will create difficulties for them while running. He prepared a table for 213 students as below.
What is the probability that a student having a knee-knock problem is also flat-footed?
a. 3/20
b. 8/113
c. 15/23
d. 15/213
a. 3/20
Case:
The CDC recommends that adults over 60 should receive the Zostavax vaccine to prevent shingles and postherpetic neuralgia (PHN).
The following data was imputed from Table 1 of the Highlights of Prescribing information report on Zostavax.
Question:
What portion of patients who received Zostavax experience local area pain?
a. 27%
b. 31%
c. 54%
d. 87%
c. 54%
The exercise times of 50 randomly selected people at the gym were recorded. In this survey, data were collected on different time slots. The histogram displays the data collected in this survey. In which of the following intervals is the median of these data located? Refer to the image.
a. Between 10 AM and 12 PM
b. Between 12 PM and 2 PM
c. Between 4 PM and 6 PM
d. Between 6 PM and 8 PM
d. Between 6 PM and 8 PM
Case:
Two random samples of students are chosen: one sample from those who were able to attempt all sections in an entry test within the given time and one sample from those who were not. The back-to-back stem plots compare the scores. The leaves on the stem plot represent decimal places. Refer to the image.
Question:
What is the difference in ranges between students who attempted all the sections and the students who did not attempt all the sections?
a. 0.2
b. 0.4
c. 1.5
d. 2.4
b. 0.4
Case:
Hospital staff recently conducted a patient satisfaction survey. The table below shows how the 94 patients surveyed answered the following prompt: “How did the staff treat you?”
Question:
What is the standard error for the proportion of patients that answered either Good or Very Good?
a. 0.0021
b. 0.046
c. 0.051
d. 6.5
b. 0.046
