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Chapter 9: 57 (page 564)

After once again losing a football game to the archrival, a college鈥檚 alumni association conducted a survey to see if alumni were in favor of firing the

coach. An SRS of 100 alumni from the population of all living alumni was taken, and 64 of the alumni in the sample were in favor of firing the coach.

Suppose you wish to see if a majority of living alumni are in favor of firing the coach. The appropriate test statistic is

a. z=0.64-0.50.64(0.36)100

b.t=0.64-0.50.64(0.36)100

c.z=0.64-0.50.5(0.5)100

d.z=0.64-0.50.64(0.36)64

e.z=0.5-0.640.5(0.5)100

Short Answer

Expert verified

Option a is correct

Step by step solution

01

Step 1. Test statsitic 

The test statistic for the population proportion is as follows:

z=p鈭�p^p1鈭�p100

where p=0.64, role="math" localid="1654256041572" p^=0.5and n=100.

02

Step 2. Substitute the value in the test statistic.

Substitute the respective values in the test statistic.

z=0.64鈭�0.50.641鈭�0.64100=0.64鈭�0.50.64脳0.36100

So, option a is the correct option.

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Most popular questions from this chapter

A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school鈥檚 students approved of the parking that was provided. After the change, the principal surveys an SRS of 200 of the over 2500 students at the school. In all, 83 students say that they approve of the new parking arrangement. The principal cites this as evidence that the change was effective. Perform a test of the principal鈥檚 claim at the 伪=0.05 significance level.

A random sample of 100likely voters in a small city produced 59voters in favor of Candidate A. The observed value of the test statistic for testing the null hypothesis H0:p=0.5versus the alternative hypothesis Ha:p=0.5is

(a)z=0.59-0.50.59(0.41)100

(b). z=0.59-0.50.5(0.5)100

(c). z=0.5-0.590.59(0.41)100

(d). z=0.5-0.590.5(0.5)100

(e).t=0.59-0.50.5(0.5)100

An SRS of 100 postal employees found that the average time these employees had worked at the postal service was 7years with standard deviation 2years. Do these data provide convincing evidence that the mean time of employment M for the population of postal employees has changed from the value of 7.5 that was true 20years ago? To determine this, we test the hypotheses H0:渭=7.5versus Ha:渭鈮�7.5using a one-sample ttest. What conclusion should we draw at the 5%significance level?

(a) There is convincing evidence that the mean time working with the postal service has changed.

(b) There is not convincing evidence that the mean time working with the postal service has changed.

(c) There is convincing evidence that the mean time working with the postal service is still 7.5 years.

(d) There is convincing evidence that the mean time working with the postal service is now 7years.

(e) We cannot draw a conclusion at the 5% significance level. The sample size is too small.

A college professor suspects that students at his school are getting less than 8 hours of sleep a night, on average. To test his belief, the professor asks a random sample of 28 students, 鈥淗ow much sleep did you get last night?鈥� Here are the data (in hours): 96868866.56794345611636610784.5977

Do these data provide convincing evidence in support of the professor鈥檚 suspicion? Carry out a significance test at the a=0.05level to help answer this question.

Refer to Exercise 2. For Yvonne's survey, 96 students in the sample said they rarely or never argue with friends. A significance test yields a P-value of 0.0291.

(a) Interpret this result in context.

(b) Do the data provide convincing evidence against the null hypothesis? Explain.
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