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Chapter 9: Q 22. (page 565)

Philly fanatics? Nationally, the proportion of red cars on the road is 0.12.A statistically minded fan of the Philadelphia Phillies (whose team color is red) wonders if Phillies fans are more likely to drive red cars. One day during a home game, he takes a random sample of 210cars parked at Citizens Bank Park (the Phillies home field), and counts 35red cars.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.

b. Explain why there is some evidence for the alternative hypothesis.

c. The P-value for the test in (a) is 0.0187. Interpret the P-value.

d. What conclusion would you make at the α=0.05 significance level?

Short Answer

Expert verified

a. H0:p=0.12and H1:p>0.12

b. Sample proportion is greater than 0.12and it corresponds to claim of alternative hypothesis.

c. There is a 1.87%confidence that 35or more out of 210randomly selected Phillies fans own a red car.

d. Enough convincing proof is present that the proportion of red cars among Phillies fans is greater than 0.12..

Step by step solution

01

Part (a) Step 1: Given Information

It is given that claim is greater than0.12.

02

Part (a) Step 2: Explanation

am

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Most popular questions from this chapter

Making conclusions A student performs a test of H0:p=0.75versus Ha:p<0.75at α=0.05significance level and gets a P-value of 0.22

The student writes: “Because the P-value is large, we accept H0. The data provide convincing evidence that null hypothesis is true". Explain what is wrong with this conclusion.

Reality TVTelevision networks rely heavily on ratings of TV shows when deciding

whether to renew a show for another season. Suppose a network has decided that

“Miniature Golf with the Stars” will only be renewed if it can be established that more than 12%of U.S. adults watch the show. A polling company asks a random sample of 2000U.S. adults if they watch “Miniature Golf with the Stars.” The network uses the data to perform a test of

H0:p=0.12

Ha:p>0.12

where pis the true proportion of all U.S. adults who watch the show. Describe a Type Ierror and a TypeIIerror in this setting, and give a possible consequence of each.

After once again losing a football game to the archrival, a college’s 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 all living alumni is in favor of firing the coach. The appropriate standardized test statistic is

(a)z=0.64-0.50.64(0.36)100z=0.64-0.50.64(0.36)100

role="math" localid="1654432946823" (b)t=0.64-0.50.64(0.36)100t=0.64-0.50.64(0.36)100

(c)z=0.64-0.50.5(0.5)100z=0.64-0.50.5(0.5)100

(d)z=0.64-0.50.64(0.36)64z=0.64-0.50.64(0.36)64

(e)z=0.5-0.640.5(0.5)100z=0.5-0.640.5(0.5)100

Attitudes Refer to Exercise 4. In the study of older students’ attitudes, the sample mean SSHA score was 125.7 and the sample standard deviation was 29.8. A significance test yields a P-value of 0.0101.

a. Explain what it would mean for the null hypothesis to be true in this setting.

b. Interpret the P-value.

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are

а.H0:p∧=0.5;Ha:p∧>0.5H0:p^=0.5;Ha:p^>0.5.

b. H0:p=0.5;Ha:p>0.5H0:p=0.5;Ha:p>0.5.

c. H0:p=0.5;Ha:p<0.5H0:p=0.5;Ha:p<0.5.

d. H0:p=0.5;Ha:p≠0.H0:p=0.5;Ha:p≠0.5.

e. H0:p>0.5;Ha:p=0.5H0:p>0.5;Ha:p=0.5.
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