Q1. As the sample size increases, the standard error of the mean increases.

a. true

b. false

Q2. The Central Limit Theorem is important in statistics because

a. for a largen, it says the population is approximately normal.

b. for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size.

c. for a largen, it says the sampling distribution of the mean is approximately normally distributed, regardless of the shape of the population distribution.

d. for any sized sample, it says the sampling distribution of the sample mean is approximately normal.

Q3. The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 64 fish yields a mean of 3.4 pounds, what is the probability of obtaining a sample mean this large or larger?

a. 0.0001

b. 0.0013

c. 0.0228

d. 0.4987

Q4. At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the standard error for the sample mean?

a. 0.029

b. 0.050

c. 0.091

d. 0.120

Q5. If the amount of gasoline purchased per car at a large service station has a population mean of $15 and a population standard deviation of $4 and a random sample of 64 cars is selected, there is approximately a 95.44% chance that the sample mean will be between $14 and $16.

a. true

b. false

Q6. Major league baseball salaries averaged $1.5 million with a standard deviation of $0.8 million in 1994. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players exceeded $1 million.

a. Approximately 0

b. 0.2357

c. 0.7357

d. Approximately 1

Q7. The average score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0. Suppose 36 golfers played the course today. Find the probability that the average score of the 36 golfers exceeded 71.

a. 0.0228

b. 0.0124

c. 0.2135

d. 0.1248

Q8. For sample size 1, the sampling distribution of the mean will be normally distributed

a. regardless of the shape of the population.

b. only if the shape of the population is symmetrical.

c. only if the population values are positive.

d. only if the population is normally distributed.

Q9. Given a sample mean of 2.1 and a sample standard deviation of 0.7 from a sample of 10 data points, a 90% confidence interval will have a width of 2.36.

a. true

b. false

Q10. In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a _____ interval.

a. narrower

b. wider

c. less significant

d. biased

Q11. Thetdistribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown.

a. true

b. false

Q12. If you were constructing a 99% confidence interval of the population mean based on a sample ofn=25 where the standard deviation of the sample standard deviation=0.05, the critical value oftwill be

a. 2.7969

b. 2.7874

c. 2.4922

d. 2.4851

Q13. A sample size of 5 provides a sample mean of 9.6. If the population variance is known to be 5 and the population distribution is assumed to be normal, the lower limit for a 92% confidence interval is 7.85.

a. true

b. false

Q14. It is desired to estimate the average total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to be ($2 million, $5 million). Which of the following interpretations is correct?

a. 97% of the sampled total compensation values fell between $2 million and $5 million.

b. We are 97% confident that the median compensation of the sampled CEOs falls in the interval $2 million to $5 million.

c. In the population of service industry CEOs, 97% of them will have total compensation that falls in the interval $2 million to $5 million.

d. We are 97% confident that the average total compensation of all CEOs in the service industry falls in the interval $2 million to $5 million.

Q15. When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 thatpis estimated to be, the __________ the sample size required.

a. larger

b. smaller

c. Sample size is not affected.

d. The effect on sample size cannot be determined from the information given.

Q16. Charities rely on money contributed by individuals and corporations for their operating expenses. Sometimes this money is put into a fund called an endowment, and the charity spends only the interest earned on these funds. A survey of 8 charities revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. What value should you use as the point estimate for the mean endowment?

a. $148

b. $181

c. $143

d. $180

Q17. For a given level of significance, if the sample size is increased, the probability of committing a Type II error will increase.

a. true

b. false

Q18. The power of a statistical test is

a.the probability of not rejectingH₀when it is false.

b. the probability of rejectingH₀when it is true.

c. the probability of not rejectingH₀when it is true.

d. the probability of rejectingH₀when it is false.

Q19. If, as a result of a hypothesis test, we reject the null hypothesis when it is false, then we have committed

a. a Type II error.

b. a Type I error.

c. no error.

d. an acceptance error.

Q20. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If she wants to be 99% confident in her decision, what rejection region should she use?

a. Reject H₀if t < -2.34

b. Reject H₀if t < -2.55

c. Reject H₀if t > 2.34

d. Reject H₀if t > 2.55

Q21. The value that separates a rejection region from a non-rejection region is called the _______.

a. significance level

b. critical value

c. test statistic

d. parameter

Q22. Which of the following would be an appropriate null hypothesis?

a. The mean of a population is equal to 55.

b. The mean of a sample is equal to 55.

c. The mean of a population is greater than 55.

d. The mean of a sample is greater than 55.

Q23. We have created a 95% confidence interval for (mu) with the result (10, 15). What decision will we make if we test H₀: = 16 versus H1: != 16, at alpha = .05? (Note: "!=" means "not equal")

a. Reject H₀

b. Accept H₀

c. Fail to reject H₀

d. Cannot tell what the decision ought to be from the information given.

Q24. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to:

a. - 4.12

b. - 2.33

c. - 1.86

d. - 0.07

Q25. A Type II error is committed when

a. we reject a null hypothesis that is true.

b. we don't reject a null hypothesis that is true.

c. we reject a null hypothesis that is false.

d. we do not reject a null hypothesis that is false.