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Chapter 9: Q. 10 (page 564)

In the study of older students鈥� attitudes, the sample mean SSHA score was 125.7and 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.

Short Answer

Expert verified

Part a. The correct mean score for the students who are at least 30years of age is 115.

Part b. The P-value is if the population mean is equal to115, then there is possibility of 1.01%of getting a random sample with a sample mean of 125.7or more.

Step by step solution

01

Part a. Step 1. Given information

From the previous exercise

H0:渭=115Ha:渭>115

02

Part a. Step 2. Explanation

渭is the population mean score of students who are at least 30years of age.

If the null hypothesis H0:渭=115is true, then this means that the true mean score for students who are at least 30years of age is115.

03

Part b. Step 1. Given information

n=45x炉=125.7s=29.8P=0.0101=1.01%

Result previous exercise:

H0:渭=115Ha:渭>115

04

Part b. Step 2. Explanation

The P-value is if the population mean is equal to 115, then there is possibility of 1.01%of getting a random sample with a sample mean of125.7 or more.

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Most popular questions from this chapter

Which of the following 95%confidence intervals would lead us to reject H0:p=0.30in favor of Ha:pnotequalto0.30at the 5%significance level?

a. (0.19,0.27)

b.(0.24,0.30)

c. (0.27,0.31)

d. (0.29,0.31)

e. None of these

No homework? Refer to Exercise 1. The math teachers inspect the

homework assignments from a random sample of 50 students at the school. Only 68% of the students completed their math homework. A significance test yields a P-value of 0.1265.

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

b. Interpret the P-value.

A95%confidence interval for the proportion of viewers of a certain reality television

show who are over 30 years old is (0.26,0.35). Suppose the show's producers want to est the hypothesis \H0:p=0.25against Ha: Ha:p鈮�0.25. Which of the following is an appropriate conclusion for them to draw at the 伪=0.05

a. Fail to reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old equals 0.25

b. Fail to reject H0there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

c. Reject H0; there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from 0.25

. d. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old is greater than 0.25.

e. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

Better parking 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 200from the more than 2500students at the school. In all, 83students say that they approve of the new parking arrangement. The principal cites this as evidence that the change was effective.

a. Describe a Type I error and a Type II error in this setting, and give a possible

consequence of each.

b. Is there convincing evidence that the principal鈥檚 claim is true?

A government report says that the average amount of money spent per U.S. household per week on food is about \(158. A random sample of50 households in a small city is selected, and their weekly spending on food is recorded. The sample data have a mean of \)165 and a standard deviation of \(20. Is there convincing evidence that the mean weekly spending on food in this city differs from the national figure of \)158?
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