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Chapter 11: Q.10 (page 693)

No chi-squareThe principal in Exercise 9also asked the random sample of students to record whether they did all of the homework that was assigned on each of the five school days that week. Here are the data:

Explain carefully why it would not be appropriate to perform a chi-square goodness-of-fit test using these data.

Short Answer

Expert verified

From the given information, the variable of interest is the average number of students who completed their homework and can give quantitative values, and the chi-square goodness of the test is used on a categorical variable, with quantitative variables. so it would not be appropriate to perform a chi-square goodness-of-fit test using these data.

Step by step solution

01

Given Information

It is given in the question that,

02

Step 2: Explanation

The variable of interest is the average number of students who completed their homework and can give quantitative values, and the chi-square goodness of the test is used on a categorical variable, with quantitative variables. As a result, chi-square goodness of fit cannot be used in this case.

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Most popular questions from this chapter

Do men and women participate in sports for the same reasons? One goal for sports participants is social comparison—the desire to win or to do better than other people. Another is mastery—the desire to improve one’s skills or to try one’s best. A study on why students participate in sports collected data from independent random samples of 67male and 67female undergraduates at a large university. Each student was classified into one of four categories based on his or her responses to a questionnaire about sports goals. The four categories were high social comparison– high mastery (HSC-HM), high social comparison– low mastery (HSC-LM), low social comparison–high mastery (LSC-HM), and low social comparison–low mastery (LSC-LM). One purpose of the study was to compare the goals of male and female students. Here are the data displayed in a two-way table:

GoalFemaleMaleHSC-HM1431HSC-LM2118LSC-HM215LSC-LM2513

(a) Calculate the conditional distribution (in proportions) of the reported sports goals for each gender.

(b) Make an appropriate graph for comparing the conditional distributions in part (a).

(c) Write a few sentences comparing the distributions of sports goals for male and female undergraduates.

Stress and heart attack You read a newspaper article that describes a study of whether stress management can help reduce heart attacks. The 107subjects all had reduced blood flow to the heart and so were at risk of a heart attack. They were assigned at random to three groups. The article goes on to say: One group took a four-month stress management program, another underwent a four-month exercise program, and the third received usual heart care from their personal physicians. In the next three years, only three of the 33people in the stress management group suffered “cardiac events,” defined as a fatal or non-fatal heart attack or a surgical procedure such as a bypass or angioplasty. In the same period, seven of the 34people in the exercise group and 12out of the 40 patients in usual care suffered such events.36

(a) Use the information in the news article to make a two-way table that describes the study results.

(b) What are the success rates of the three treatments in preventing cardiac events?

(c) Is there a significant difference in the success rates for the three treatments? Give appropriate statistical evidence to support your answer.

A company claims that each batch of its deluxe mixed nuts contains 52%cashews, 27%almonds, 13%macadamia nuts, and 8%brazil nuts. To test this claim, a quality control inspector takes a random sample of 150nuts from the latest batch. The one-way table below displays the sample data.

(a) State appropriate hypotheses for performing a test of the company’s claim.

(b) Calculate the expected counts for each type of nut. Show your work

Calculate the chi-square statistic for Joey’s sample. Show your work

Why is it important to compare proportions rather than counts in Question 1?
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