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

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 H_{0}: *μ* = 16 versus H_{a}: *μ* ≠ 16 at *α* = 0.05?

A) Reject H_{0}

B) Accept H_{0}

C) Fail to reject H_{0}

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

7. Suppose we want to test H_{0}: *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 H_{0} 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.

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