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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

Two-sided test The one-sample t statistic from a sample of n=25observations for the two-sided test of H0:渭=64;Ha:渭鈮�64has the value t=-1.12.

(a) Find the P-value for this test using (i) Table Band (ii) your calculator. What conclusion would you draw at the 5%significance level? At the 1%significance level?

(b) Redo part (a) using an alternative hypothesis of Ha:渭<64.

Refer to Exercise 1. In Simon鈥檚 SRS, 16 of the students were left-handed. A significance test yields a P-value of 0.2184.

(a) Interpret this result in context.

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

Anemia For the study of Jordanian children in Exercise 64, the sample mean hemoglobin level was 11.3mg/dl and the sample standard deviation was 1.6mg/dl.

(a) Calculate the test statistic.

(b) Find the P-value using Table B. Then obtain a

more precise P-value from your calculator.

A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of one inch could be increased by

(a) using only volunteers from the basketball team in the experiment.

(b) using A=0.01 instead of A=0.05.

(c) using A=0.05 instead of A=0.01.

(d) giving the drug to 25 randomly selected students instead of 50.

(e) using a two-sided test instead of a one-sided test.

Explain why we aren't safe carrying out a one-sample z test for the population proportion p.

You toss a coin 10 times to test the hypothesis H0:p=0.5 that the coin is balanced.
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