PART A
1. A researcher conducts a study to investigate the effect of exercise and diet on mood. The factors in this study are
A) whether randomization and placeboes were used.
B) whether the experiment was double blind.
C) the number of subjects.
D) exercise and diet.
Use the following to answer questions 2-3:
A psychologist studied the number of puzzles subjects were able to solve in a 5-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. The psychologist found that X had the following probability distribution.
Value of X 1 2 3 4
Probability 0.2 0.4 0.3 0.1
2. The probability that a randomly chosen subject completes at least 3 puzzles in the 5-minute period while listening to soothing music is
A) 0.3. B) 0.4. C) 0.6. D) 0.9.
3. P(X < 3) has value
A) 0.3. B) 0.4. C) 0.6. D) 0.9.
4. The distribution of actual weights of 8-oz. chocolate bars produced by a certain machine is normal with mean 8.1 ounces and standard deviation 0.1 ounces. If a sample of five of these chocolate bars is selected, the probability that their average weight is less than 8 oz. is
A) 0.0125. B) 0.1853. C) 0.4871. D) 0.9873.
5. The law of large numbers states that, as the number of observations drawn at random from a population with finite mean m increases, the mean J of the observed values
A) gets larger and larger.
B) gets smaller and smaller.
C) gets closer and closer to the population mean m.
D) fluctuates steadily between one standard deviation above and one standard deviation below the mean.
Use the following to answer questions 6-7:
I roll a pair of fair dice and compute the number of spots on the two sides facing up. Denote this total by X. The probability distribution of X is
6. The probability that X is a 2, 11, or 12 is
A) 1/36. B) 2/36 C) 3/36. D) 4/36.
7. The probability that X is at least 7 is
A) 5/36 B) 6/36. C) 15/36 D) 21/36.
8. The incomes in a certain large population of college teachers have a normal distribution with mean $35,000 and standard deviation $5000. Four teachers are selected at random from this population to serve on a salary review committee. What is the probability that their average salary exceeds $40,000?
A) .0228 B) .1587 C) .9772 D) essentially 0
9. Twenty-five seniors from a large metropolitan area school district volunteer to allow their Math SAT test scores to be used in a study. These twenty-five seniors had a mean Math SAT score of J = 450. Suppose we know that the standard deviation of the population of Math SAT scores for seniors in the district is s = 100. Assuming the population of Math SAT scores for seniors in the district is approximately normally distributed, a 90% confidence interval for the mean Math SAT score m for the population of seniors computed from these data is
A) 450 ± 32.9. B) 450 ± 39.2. C) 450 ± 164.5. D) not trustworthy.
10. A certain population follows a normal distribution with mean m and standard deviation s = 2.5. You collect data and test the hypotheses
H0: m = 1, Ha: m ¹ 1.
You obtain a P-value of 0.022. Which of the following is true?
A) A 95% confidence interval for m will include the value 1
B) A 95% confidence interval for m will include the value 0
C) A 99% confidence interval for m will include the value 1
D) A 99% confidence interval for m will include the value 0
11. The mean area m of the several thousand apartments in a new development is advertised to be 1250 square feet. A tenant group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicion. The appropriate null and alternative hypotheses, H0 and Ha, for m
A) are H0: m = 1250 and Ha: m ¹ 1250.
B) are H0: m = 1250 and Ha: m < 1250.
C) are H0: m = 1250 and Ha: m > 1250.
D) cannot be specified without knowing the size of the sample used by the engineer.
Use the following to answer questions 12-13:
The heights of young American women, in inches, are normally distributed with mean m and standard deviation s = 2.4. I select a simple random sample of four young American women and measure their heights. The four heights, in inches, are
63 69 62 66
12. If I want the margin of error for a 99% confidence interval to be ± 1 inch, I should select a simple random sample of size
A) 2. B) 7. C) 16. D) 39.
13. Based on these data, a 99% confidence interval for m, in inches, is
A) 65.00 ± 1.55. B) 65.00 ± 2.35. C) 65.00 ± 3.09. D) 65.00 ± 4.07.
14. A probability sample is any sample in which
A) every member of the population has the same chance of being selected.
B) every member of the population has a known, nonzero chance of being selected.
C) the population is first divided into groups of similar individuals, and then a separate simple random sample is selected from each group and combined to form the full sample.
D) all collections of members of the population have the same chance of being selected.
15. The level of calcium in the blood of healthy young adults follows a normal distribution with mean m = 10 milligrams per deciliter and standard deviation s = 0.4. A clinic measures the blood calcium of 100 healthy pregnant young women at their first visit for prenatal care. The mean of these 100 measurements is J = 9.8. Is this evidence that the mean calcium level in the population from which these women come is less than 10? To answer this, test the hypotheses
H0: m = 10, Ha: m < 10.
The P-value of your test is
A) less than 0.0002. B) 0.3085. C) 0.6170. D) greater than 0.99.
16. The sampling distribution of a statistic is
A) the probability that we obtain the statistic in repeated random samples.
B) the mechanism that determines whether or not randomization was effective.
C) the distribution of values taken by a statistic in all possible samples of the same size from the same population.
D) the extent to which the sample results differ systematically from the truth.
Answer Key -- exam_2
1. D
2. B
3. C
4. A
5. C
6. D
7. D
8. A
9. D
10. C
11. B
12. D
13. C
14. B
15. A
16. C