If the sampling distribution of a sample statistic has a mean equal to the

1. If the sampling distribution of a sample statistic has a mean equal to the parameter it is estimating, then we call that sample statistic

A) Unbiased.

B) Confident.

C) Biased.

D) Random.

2. A sample of n = 15 items is drawn from a population of manufactured products and the weight of each item is recorded. Prior experience has shown that the weight has a probability distribution with μ = 6 ounces and σ = 2.5 ounces. Which of the following is true about the sampling distribution of the sample mean?

A) The mean of the sampling distribution is 6 ounces.

B) The standard deviation of the sampling distribution is 2.5 ounces.

C) The shape of the sampling distribution is approximately normal.

D) All of the above are correct.

3. Suppose a 95% confidence interval for μ has been constructed. If it is decided to take a larger sample and to decrease the confidence level of the interval, then the resulting interval width would ________. (Assume that the sample statistics gathered would not change very much for the new sample.)

A) be larger than the current interval width

B) be narrower than the current interval width

C) be the same as the current interval width

D) be unknown until actual sample sizes and reliability levels were determined

4. Which of the following could 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) Both A and B are appropriate.

5. If an economist wishes to determine whether there is evidence that mean family income in a community exceeds $50,000

A) either a one-tail or two-tail test could be used with equivalent results.

B) a one-tail test should be used.

C) a two-tail test should be used.D) a regression analysis should be performed.

6. We have created a 95% confidence interval for μ with the result (12, 17). What decision will we make if we test H₀: μ = 16 versus H_a: μ ≠ 16 at α = 0.05?

A) Reject H₀

B) Accept H₀

C) Fail to reject H₀

D) We cannot tell what our decision will be from the information given

7. Suppose we want to test H₀: μ = 30 versus H_a: μ< 30. Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H₀ in favor of H_a?

A) = 28, S = 6

B)  = 27, S = 4

C)  = 32, S = 2

D) = 26, S = 9

8. A major DVD rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. What is the alternative hypothesis (H_a) the chain will use in a hypothesis test?

A) p> 0.32

B) p> 0.25

C) p> 5,000

D) μ> 5,000

9. A manager of the credit department for an oil company states that the mean monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the mean owed is $83.40 with a sample standard deviation of $23.65. If you wanted to test whether there is evidence that the mean balance is different from $75, which test would you use?

A) Z-test of a population mean

B) Z-test of a population proportion

C) t-test of a population mean

D) t-test of a population proportion

10. If the p-value is less than α in a two-tail test,

A) the null hypothesis should not be rejected.

B) the null hypothesis should be rejected.

C) a one-tail test should be used.

D) no conclusion can be reached.

11. In order to construct a 99% confidence interval, what critical t-value should you use if your sample size is 15?

12. The standard deviation of the sampling distribution of the sample proportion will be ______times bigger for sample size 25 compared to sample size 100.

13. In a two-tail hypothesis test with a sample size of 36, the test statistic is computed to be z = 2.17. What is the p-value?

14. In a one-tail hypothesis test with a sample size of 64, the test statistic is computed to be t = -1.75. What is the p-value?

15. Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars):

   60.2    87.0    235.1    190.0    122.6    177.5    95.4    220.0

What value will be used as the point estimate for the mean endowment of all private colleges in the United States?

16. Using the information in the previous question, set up a 99% confidence interval estimate of the mean endowment of all private colleges in the United States. Show your work.

17. In constructing the confidence interval in the previous question, what was your margin of error?

18. A survey of students at a small college found that:

     45% of the students were males

     40% of the students smoked

     25% of the students were males and smokers

What is the probability that a student chosen at random is either a male or a smoker?

19. A student is taking a short multiple-choice quiz in which each question has five choices - - A, B, C, D, E. The student hasn’t studied so he randomly selects an answer for each of the 4 questions.

What is the probability that he gets at least one answer correct?

20. At a large department store, the average number of years of employment for a cashier is 5.6 with a standard deviation of 1.8 years, and the distribution is approximately normal. If an employee is picked at random, what is the probability that the employee has worked at the store for less than 4 years?

21. At the department store in the previous question, a random sample of 10 employees is selected. What is the probability that their average length of employment is more than 7 years?

22. The average teacher’s salary in Ohio is $53,309. Assume the population distribution of salaries has a standard deviation of $6,200. If a random sample of 150 Ohio teachers had a mean salary of $54,800, would you be surprised? EXPLAIN.

23. In order to answer the previous question, was it necessary to assume that the population had a normal distribution? EXPLAIN.

24. The manager of a company is worried about the morale of her employees. In order to determine if a problem in this area exists, she decides to evaluate the attitudes of the employees with a standardized test of job satisfaction which is known to have a normal distribution with a standard deviation of 22 points. How large a sample of employees is needed in order to estimate the mean of all employees using a 99% confidence interval with a length of 6.8 points?

25. The sample proportion obtained from a sample of 1550 individuals will differ from the true proportion by no more than ______%.

26. A quality control engineer is interested in estimating the proportion of defective items coming off a production line. In a sample of 250 items, 27 are defective. A 90% confidence interval for the proportion of defectives from this production line would go from ________ to ________.

27. A drug company advertises that 9 out of 10 doctors recommend aspirin for their patients with headaches. A consumer agency decides to survey a random sample of doctors to see if there is evidence that fewer than 9 out of 10 doctors actually recommend aspirin.

State the null and alternative hypotheses.

28. State the null and alternative hypotheses.

29. Should you be using z or t? EXPLAIN.

30. What is the value of the test statistic? (Show your work).

31. What is the p-value?

32. What is your statistical decision? EXPLAIN.

33. What should the nightclub owner do?

EXPLAIN.