Question: To determine the average number of children living in single-family homes, a researcher picks a simple random sample of 50 such homes. However, even after one follow-up visit the interviewer is unable to make contact with anyone in 8 of these homes. Concerned about nonresponse bias, the researcher picks another simple random sample and instructs the interviewer to keep trying until contact is made with someone in a total of 50 homes. The average number of children is determined to be 1.73. Is this estimate probably too low or too high?

Choices:
- Too low, because of undercoverage bias.
- Too low, because convenience samples overestimate average results.
- Too high, because of undercoverage bias.
- Too high, because convenience samples overestimate average results.


Question: If all the values of a data set are the same, all of the following must equal zero except for which one?

Choices:
- Mean
- Standard deviation
- Variance
- Range


Question: A university sent out a survey to a random sample of 120 recent graduates to see how those graduates feel about the education they received. Thirty-two of the graduates did not respond to the survey. Which of these would be the best way to proceed?

Choices:
- Use the 88 who did respond, using 88 as the sample size in the analysis.
- Use the 88 who did respond, using 120 as the sample size in the analysis.
- Attempt to contact the 32 who did not respond and get the information from them.
- Select 32 more graduates at random and use them to replace the nonresponders.


Question: Given the probabilities P(A) = 0.3 and P(B) = 0.2, what is the probability of the union P(A ∪ B) if A and B are mutually exclusive? If A and B are independent? If B is a subset of A?

Choices:
- 0.44, 0.5, 0.2
- .44, 0.5, 0.3
- .5, 0.44, 0.2
- .5, 0.44, 0.3


Question: Which of the following is true about any discrete probability distribution of a random variable X?

Choices:
- The expected value of X = np.
- The sum of all possible values of X is equal to one.
- The probabilities of all possible values of X must add up to one.
- The probability distribution is bell-shaped and symmetric.


Question: Which among the following would result in the narrowest confidence interval?

Choices:
- Small sample size and 95% confidence
- Small sample size and 99% confidence
- Large sample size and 95% confidence
- Large sample size and 99% confidence


Question: The correlation between height in inches and weight in pounds for a particular class is 0.65. If the heights are converted from inches to centimeters, what will the correlation be? (1 in. = 2.54 cm)

Choices:
- -0.65
- -0.26
- 0.1
- 0.65


Question: The number of days it takes to build a new house has a variance of 386. A sample of 40 new homes shows an average building time of 83 days. With what confidence can we assert that the average building time for a new house is between 80 and 90 days?

Choices:
- 15.4%
- 17.8%
- 20.0%
- 82.1%


Question: A significance test of the hypothesis H0: p= 0.3 against the alternative HA: p> 0.3 found a value of = 0.35 for a random sample of size 95. What is the P-value of this test?

Choices:
- 1.06
- 0.1446
- 0.2275
- 0.8554


Question: Two events A and B each have a nonzero probability. If A and B are independent, which of the following statements is true?

Choices:
- P(A and B) = P(A) · P(B)
- A and B may or may not be mutually exclusive.
- A and B must be mutually exclusive.
- P(A| B) = P(B| A)


Question: A teacher believes that giving her students a practice quiz every week will motivate them to study harder, leading to a greater overall understanding of the course material. She tries this technique for a year, and everyone in the class achieves a grade of at least C. Is this an experiment or an observational study?

Choices:
- An experiment, but with no reasonable conclusion possible about cause and effect
- An experiment, thus making cause and effect a reasonable conclusion
- An observational study, because there was no use of a control group
- An observational study, but a poorly designed one because randomization was not used


Question: Which of these is the best description of a P-value?

Choices:
- The probability of making a Type I error.
- The probability of making a Type II error.
- The probability of rejecting the null hypothesis if it is, in fact, false.
- The probability of getting a test statistic at least as extreme as the observed test statistic, if the null hypothesis is true.


Question: The financial aid office at a state university conducts a study to determine the total student costs per semester. All students are charged $4500 for tuition. The mean cost for books is $350 with a standard deviation of $65. The mean outlay for room and board is $2800 with a standard deviation of $380. The mean personal expenditure is $675 with a standard deviation of $125. Assuming independence among categories, what is the standard deviation of the total student costs?

Choices:
- $24
- $91
- $190
- $405


Question: Self-efficacy (the belief that one has control over one's situation) as it related to job satisfaction was studied. When a group of teachers rated their ability to control their situation and their satisfaction with their job, the two variables had a correlation of 0.30. Which statement follows from this correlation?

Choices:
- If you want teachers to be happy with their job, give them more control over their situation.
- If you want teachers to take more control over their situation, make them happier at their jobs.
- Teachers in the study who were more satisfied with their job were less confident in their ability to control their situation.
- 9% of the variability in job satisfaction can be explained by the linear model with self-efficacy as a predictor.


Question: Suppose X and Y are random variables with E(X) = 312, var(X) = 6, E(X) = 307, and var(Y) = 8. What are the expected value and variance of the random variable X + Y?

Choices:
- E(X + Y) = 619, var(X + Y) = 7
- E(X + Y) = 619, var(X + Y) = 10
- E(X + Y) = 619, var(X + Y) = 14
- There is insufficient information to answer this question.


Question: Consider the two sets X = {10, 30, 45, 50, 55, 70, 90} and Y = {10, 30, 35, 50, 65, 70, 90}. Which of the following is false?

Choices:
- The sets have identical medians.
- The sets have identical means.
- The sets have identical ranges.
- None of the above are false.


Question: Which of the following is a true statement?

Choices:
- In a well-designed, well-conducted sample survey, sampling error is effectively eliminated.
- In a well-designed observational study, responses are influenced through an orderly, carefully planned procedure during the collection of data.
- In a well-designed experiment, the treatments are carefully planned to result in responses that are as similar as possible.
- None of the above is a true statement.


Question: A researcher is hoping to find a predictive linear relationship between the explanatory and response variables in her study. Accordingly, as part of her analysis she plans to generate a 95% confidence interval for the slope of the regression line for the two variables. The interval is determined to be (0.45, 0.80). Which of the following is (are) true? (Assume conditions for inference are met.) I. She has good evidence of a linear relationship between the variables. II. It is likely that there is a non-zero correlation (r) between the two variables. III. It is likely that the true slope of the regression line is 0.

Choices:
- I and II only
- I and III only
- II and III only
- I only


Question: A student organization at a university is interested in estimating the proportion of students in favor of showing movies biweekly instead of monthly. How many students should be sampled to get a 90 percent confidence interval with a width of at most 0.08?

Choices:
- 27
- 64
- 106
- 423


Question: A correlation of 0.6 indicates that the percentage of variation in y that is explained by the variation in x is how many times the percentage indicated by a correlation of 0.3?

Choices:
- 2
- 3
- 4
- 6


Question: For which of the following is it appropriate to use a census?

Choices:
- A 95% confidence interval of mean height of teachers in a small town.
- A 95% confidence interval of the proportion of students in a small town who are taking some AP class.
- A two-tailed hypothesis test where the null hypothesis was that the mean expenditure on entertainment by male students at a high school is the same as that of female students.
- None of the above.


Question: Which of the following is the best description of the power of a significance test?

Choices:
- The probability that the null hypothesis is true.
- The probability of getting a Type I error.
- The probability of getting a Type II error.
- The probability of rejecting the null hypothesis if it is, in fact, false.


Question: A drug company will conduct a randomized controlled study on the effectiveness of a new heart disease medication called Heartaid. Heartaid is more expensive than the currently used medication. The analysis will include a significance test with H0: Heartaid and the current medication are equally effective at preventing heart disease and HA: Heartaid is more effective than the current medication at preventing heart disease. Which of these would be a potential consequence of a Type II error?

Choices:
- Patients will spend more money on Heartaid, even though it is actually not any more effective than the current medication.
- Doctors will begin to prescribe Heartaid to patients, even though it is actually not any more effective than the current medication.
- Patients will continue to use the current medication, even though Heartaid is actually more effective.
- Researchers will calculate the wrong P-value, making their advice to doctors invalid.


Question: Two classes take the same exam. Suppose a certain score is at the 40th percentile for the first class and at the 80th percentile for the second class. Which of the following is the most reasonable conclusion?

Choices:
- Students in the first class generally scored higher than students in the second class.
- Students in the second class generally scored higher than students in the first class.
- A score at the 20th percentile for the first class is at the 40th percentile for the second class.
- A score at the 50th percentile for the first class is at the 90th percentile for the second class.


Question: The mean thrust of a certain model jet engine is 9500 pounds. Concerned that a production process change might have lowered the thrust, an inspector tests a sample of units, calculating a mean of 9350 pounds with a z-score of -2.46 and a P-value of 0.0069. Which of the following is the most reasonable conclusion?

Choices:
- 99.31% of the engines produced under the new process will have a thrust under 9350 pounds.
- 99.31% of the engines produced under the new process will have a thrust under 9500 pounds.
- 0.69% of the time an engine produced under the new process will have a thrust over 9500 pounds.
- There is evidence to conclude that the new process is producing engines with a mean thrust under 9500 pounds.


Question: When the point (15,2) is included, the slope of regression line (y= a+ bx) is b= -0.54. The correlation is r= -0.82. When the point is removed, the new slope is -1.04 and the new correlation coefficient is -0.95. What name is given to a point whose removal has this kind of effect on statistical calculations?

Choices:
- Outlier
- Statistically significant point
- Point of discontinuity
- Influential point