15.

A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage, the mean, of foodservice workers in the U.S. Last year's mean hourly wage was $ 8.25, and there is reason to believe that this year's value is less than last year's.

The union decides to do a statistical test to see if the value has indeed decreased. The union chooses a random sample of this year's wages, computes the mean of the sample to be $ 7.98 , and computes the standard deviation of the sample to be $ 1.20.

Based on this information, answer the questions below.

What are the null hypothesis () and the alternative hypothesis () that should be used for the test?

In the context of this test, what is a Type II error?

A Type II error is, the hypothesis thatis,when, in fact,is

Suppose that the union decides to reject the null hypothesis. What sort of error might it be making?

16. The records of a casualty insurance company show that, in the past, its clients have had a mean of1.9 auto accidents per day with a variance of 0.0025. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0025 . Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.

H0 = ___H1____

17. A laboratory claims that the mean sodium level,mean , of a healthy adult is 141 mEqper liter of blood. To test this claim, a random sample of 100 adult patients is evaluated. The mean sodium level for the sample isper liter of blood. It is known that the population standard deviation of adult sodium levels is 10 mEq . Can we conclude, at the 0.01level of significance, that the population mean adult sodium level differs from that claimed by the laboratory?

Perform a two-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places, and round your responses as specified below.

(a) State the null hypothesisH0and the alternative hypothesisH1.

(b) Determine the type of test statistic to use.

(c) Find the value of the test statistic. (Round to three or more decimal places.)

(d) Find the two critical values. (Round to three or more decimal places.)

(e) Can we conclude that the population mean adult sodium level differs from that claimed by the laboratory?Yes No

18. An electronics manufacturing process has a scheduled mean completion time of75 minutes. It is claimed that, under new management, the mean completion time,mean , is less than75 minutes. To test this claim, a random sample of 20completion times under new management was taken.

The sample had a mean completion time of 74 minutes and a standard deviation of 12 minutes. Assume that the population of completion times under new management is normally distributed. At the 0.05level of significance, can it be concluded that the mean completion time,mean , under new management is less than the scheduled mean?

Perform a one-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

(a) State the null hypothesis H0 and the alternative hypothesis H1 .

(b) Determine the type of test statistic to use.

(c) Find the value of the test statistic. (Round to three or more decimal places.)

(d) Find the critical value. (Round to three or more decimal places.)

(e) At the 0.05 level, can it be concluded that the mean completion time under new management is less than the scheduled mean? Yes or No

19. A presidential candidate's aide estimates that, among all college students, the proportionp who intend to vote in the upcoming election is at least 70%.If 145 out of a random sample of235 college students expressed an intent to vote, can we reject the aide's estimate at the 0.01 level of significance?

Perform a one-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places and round your answers as specified in the table.

(a) State the null hypothesis H0 and the alternative hypothesis H1 .

(b) Determine the type of test statistic to use.

(c) Find the value of the test statistic. (Round to three or more decimal places.)

(d) Find the p-value. (Round to three or more decimal places.)

(e) Can we reject the aide's estimate that the proportion of college students who intend to vote is at least 70 ?Yes orNo

20. A decade-old study found that the proportion,p , of high school seniors who believed that "getting rich" was an important personal goal was70% . A researcher decides to test whether or not that percentage still stands. He finds that, among the 215 high school seniors in his random sample,153 believe that "getting rich" is an important goal. Can he conclude, at the 0.05level of significance, that the proportion has indeed changed?

Perform a two-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places and round your answers as specified in the table.

(a) State the null hypothesis H0 and the alternative hypothesis H1 .

(b) Determine the type of test statistic to use.

(c) Find the value of the test statistic. (Round to three or more decimal places.)

(d) Find the two critical values. (Round to three or more decimal places.)

(e) Can we conclude that the proportion of high school seniors who believe that "getting