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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

A company that manufactures classroom chairs for high school students

claims that the mean breaking strength of the chairs is 300 pounds. One of the chairs collapsed beneath a 220-pound student last week. You suspect that the manufacturer is exaggerating the breaking strength of the chairs, so you would like to perform a test of H0:渭=300Ha:渭<300where 渭 is the true mean breaking strength of this company鈥檚 classroom chairs.

a. The power of the test to detect that 渭=294 based on a random sample of 30

chairs and a significance level of 伪=0.05 is 0.71. Interpret this value.

b. Find the probability of a Type I error and the probability of a Type II error for the test in part (a).

c. Describe two ways to increase the power of the test in part (a).

Watching grass grow The germination rate of seeds is defined as the proportion of seeds that sprout and grow when properly planted and watered. A certain variety of grass seed usually has a germination rate of 0.80. A company wants to see if spraying the seeds with a chemical that is known to increase germination rates in other species will increase the germination rate of this variety of grass. The company researchers spray a random sample of 400grass seeds with the chemical, and 339of the seeds germinate. Do these data provide convincing evidence at the 伪=0.05 significance level that the chemical is

effective for this variety of grass?

Jump around Student researchers Haley, Jeff, and Nathan saw an article on the Internet claiming that the average vertical jump for teens was 15 inches. They wondered if the average vertical jump of students at their school differed from 15 inches, so they obtained a list of student names and selected a random sample of 20 students. After contacting these students several times, they finally convinced them to allow their vertical jumps to be measured. Here are the data (in inches):

Do these data provide convincing evidence at the 伪=0.10 level that the average vertical jump of students at this school differs from 15 inches?

Restaurant power Refer to Exercise 86 Determine if each of the following changes would increase or decrease the power of the test. Explain your answers.

a. Use a random sample of 30 people instead of 50 people.

b. Try to detect that 渭=\(85,500 instead of 渭=\)86,000

c. Change the significance level to 伪=0.10

Paying high prices? A retailer entered into an exclusive agreement with a supplier who guaranteed to provide all products at competitive prices. To be sure the supplier honored the terms of the agreement, the retailer had an audit performed on a random sample of 25 invoices. The percent of purchases on each invoice for which an alternative supplier offered a lower price than the original supplier was recorded.17 For example, a data value

of 38 means that the price would be lower with a different supplier for 38% of the items on the invoice. A histogram and some numerical summaries of the data are shown here. The retailer would like to determine if there is convincing evidence that the mean percent of purchases for which an alternative supplier offered lower prices is greater than 50% in the population of this company鈥檚 invoices.

a. State appropriate hypotheses for the retailer鈥檚 test. Be sure to define your parameter.

b. Check if the conditions for performing the test in part (a) are met.
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