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Chapter 9: Q 48. (page 582)

Proposition XA political organization wants to determine if there is convincing evidence that a majority of registered voters in a large city favor Proposition X. In an SRS of 1000registered voters, 482favor the proposition. Explain why it isn鈥檛 necessary to carry out a significance test in this setting.

Short Answer

Expert verified

Sample proportion is less than0.5

Step by step solution

01

Given Information

It is given that n=1000

x=482

Claim is greater than50%

02

Explanation and Calculation

As per given data:

Null Hypothesis: H0:p=50%=0.5

Alternative Hypothesis: H1:p>0.5

Sample proportion is calculated as:

p^=xn=4821000=0.485

Claim is population proportion less than 0.5. Sample proportion after calculation is less than 0.5.

So, there is no proof given by sample proportion that alternative hypothesis could be true.

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Most popular questions from this chapter

You are testing H0:渭=10 against Ha:渭鈮�10 based on an SRS of 15

observations from a Normal population. What values of the t statistic are statistically significant at the 伪=0.005 level?

a.t>3.326b.t>3.286c.t>2.977d.t<鈭�3.326ort>3.326e.t<鈭�3.286ort>3.286

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

邪.H0:p鈭�=0.5;Ha:p鈭�>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鈮�0.H0:p=0.5;Ha:p鈮�0.5.

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

Teens and sex The Gallup Youth Survey asked a random sample of U.S. teens aged 13 to 17 whether they thought that young people should wait until marriage to have sex.14 The Minitab output shows the results of a significance test and a 95% confidence interval based on the survey data.

a. Define the parameter of interest.

b. Check that the conditions for performing the significance test are met in this case.

c. Interpret the P-value.

d. Do these data give convincing evidence that the actual population proportion differs from 0.5? Justify your answer with appropriate evidence.

Based on the P-value in Exercise 31, which of the following would be the most

appropriate conclusion?

a. Because the P-value is large, we reject H0. We have convincing evidence that more than 50%of city residents support the tax increase.

b. Because the P-value is large, we fail to reject H0. We have convincing evidence that more than 50%of city residents support the tax increase.

c. Because the P-value is large, we reject H0. We have convincing evidence that at most 50%of city residents support the tax increase.

d. Because the P-value is large, we fail to reject H0. We have convincing evidence that at most 50%of city residents support the tax increase.

e. Because the P-value is large, we fail to reject H0. We do not have convincing

evidence that more than 50%of city residents support the tax increase.

Heavy bread? The mean weight of loaves of bread produced at the bakery where you work is supposed to be 1pound. You are the supervisor of quality control at the bakery, and you are concerned that new employees are producing loaves that are too light. Suppose you weigh an SRS of bread loaves and find that the mean weight is 0.975pound.

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 part (a) is 0.0806. Interpret the P-value.

d. What conclusion would you make at the 伪=0.01 significance level?
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