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Chapter 11: Q. R 11.5 (page 763)

Popular kids Who were the popular kids at your elementary school? Did they get good grades or have good looks? Were they good at sports? A study was performed in Michigan to examine the factors that determine social status for children in grades 4,5,and 6. Researchers administered a questionnaire to a random sample of 478students in these grades. One of the questions asked, "What would you most like to do at school: make good grades, be good at sports, or be popular?" The two-way table summarizes the students' responses. Is there convincing evidence of an association between gender and goal for students in grades 4,5,and 6?

Short Answer

Expert verified

Yes, there is a piece of convincing evidence for the association between goals and gender.

Step by step solution

01

Given information

We need to find out whether there is convincing evidence for the given data or not.

02

Explanation

We know that

The null hypothesis asserts that the variables are unrelated, whereas the alternative hypothesis asserts that they are.

H0represents there is an association between goals and gender.

H伪 represents there is no association between goals and gender.

And expected frequencies are a product of row and column total divided by table total.

And The squared differences between the actual and predicted frequencies, divided by the expected frequency, make up the chi-square subtotals.

Therefore, there is a piece of convincing evidence for the association between goals and gender.

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Most popular questions from this chapter

Opinions about the death penaltyThe General Social Survey (GSS) asked separate random samples of people with only a high school degree and people with a bachelor鈥檚 degree, 鈥淒o you favor or oppose the death penalty for persons convicted of murder?鈥� Of the 1379people with only a high school degree, 1010 favored the death penalty, while 319of the 504people with a bachelor鈥檚 degree favored the death penalty. We can test the hypothesis of 鈥渘o difference鈥� in support for the death penalty among people in these educational categories in two ways: with a two-sample z test or with a chi-square test.

a. State appropriate hypotheses for a chi-square test.

b. Here is Minitab output for a chi-square test. Interpret the P-value. What conclusion would you draw?

c. Here is Minitab output for a two-sample z test. Explain how these results are consistent with the test in part (a).

Cocaine addicts need cocaine to feel any pleasure, so perhaps giving them an antidepressant drug will help. A 3-year study with 72chronic cocaine users compared an antidepressant drug called desipramine with lithium (a standard drug to treat cocaine addiction) and a placebo. One-third of the subjects were randomly assigned to receive each treatment. At the end of the study, researchers recorded whether or not the subjects relapsed. Which of the following conditions must be satisfied to perform the appropriate chi-square test using the data from this study?

I. The population distribution is approximately Normal.

II. The treatments were randomly assigned.

III. The observed counts are all at least 5.

a. I only

b. II only

c. III only

d. II and III

e. I, II, and III

Roulette Casinos are required to verify that their games operate as advertised. American roulette wheels have 38 蝉濒辞迟蝉鈥�18 red, 18 black, and 2 green. In one casino, managers record data from a random sample of 200 spins of one of their American roulette wheels. The table displays the results.

a. State appropriate hypotheses for testing whether these data give convincing evidence that the distribution of outcomes on this wheel is not what it should be.

b. Calculate the expected count for each color.

c. Calculate the value of the chi-square test statistic.

Do students who read more books for pleasure tend to earn higher grades in English? The boxplots show data from a simple random sample of 79 students at a large high school. Students were classified as light readers if they read fewer than 3 books for pleasure per year. Otherwise, they were classified as heavy readers. Each student鈥檚 average English grade for the previous two

marking periods was converted to a GPA scale, where A=4.0, A鈭�=3.7, B+=3.3

Reading and grades (3.2) The scatterplot shows the number of books read and the English grade for all 79 students in the study. The least-squares regression line y^=3.42+0.024x has been added to the graph.

a. Interpret the slope and y intercept.

b. The student who reported reading 17 books for pleasure had an English GPA of 2.85. Calculate and interpret this student鈥檚 residual.

c. For this linear model, r2=0.083 Interpret this value.

The two-way table shows the results of the experiment described in

Exercise 28.

Hatching Statuswater temperature:coldwater temperature:neutral
water temperature:hot
Total
Yes16
38
75
129
No11
18
29
58
Total
27
56
104
187

a. State the appropriate null and alternative hypotheses.

b. Show the calculation for the expected count in the Cold/Yes cell. Then provide a

complete table of expected counts.

c. Calculate the value of the chi-square test statistic.
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