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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.

Hα 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

The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the new school year. She wants to know if each type of food will be equally popular so she can start ordering supplies and making other plans. To find out, she selects a random sample of 100students and asks them, “Which type of food do you prefer: Ramen, tacos, pizza, or hamburgers?” Here are her data:

The chi-square test statistic is

a. (18−25)225+(22−25)225+(39−25)225+(21−25)225

b. (25−18)218+(25−22)222+(25−39)239+(25−21)221

c. (18−25)25+(22−25)25+(39−25)25+(21−25)25

d. (18−25)2100+(22−25)2100+(39−25)2100+(21−25)2100

e. (0.18−0.25)20.25+(0.22−0.25)20.25+(0.39−0.25)20.25+(0.21−0.25)20.25

A Type I error would occur if we found convincing evidence that

a. HCC wiring caused cancer when it actually didn’t.

b. HCC wiring didn’t cause cancer when it actually did.

c. there is no association between the type of wiring and the form of cancer when there actually is an association.

d. there is an association between the type of wiring and the form of cancer when there actually is no association.

e. the type of wiring and the form of cancer have a positive correlation when they actually don’t.

Where do young adults live? A survey by the National Institutes of Health asked a random sample of young adults (aged 19to 25years), “Where do you live now? That is, where do you stay most often?” Here is the full two-way table (omitting a few who refused to answer and one who reported being homeless):

a. Should we use a chi-square test for homogeneity or a chi-square test for independence in this setting? Justify your answer.

b. State appropriate hypotheses for performing the type of test you chose in part (a). Here is Minitab output from a chi-square test.

c. Check that the conditions for carrying out the test are met.

d. Interpret the P-value. What conclusion would you draw?

P-values For each of the following, find the P-value using Table C Then

calculate a more precise value using technology.

a. χ2=19.03,df=11

b. χ2=19.03,df=3

The color of candy Inspired by the example about how background music influences

choice of entrée at a restaurant, a statistics student decided to investigate other ways to

influence a person’s behavior. Using 60volunteers, she randomly assigned 20volunteers

to get a “red” survey, 20volunteers to get a “blue” survey, and 20volunteers to get a

control survey. The first three questions on each survey were the same, but the fourth and

fifth questions were different. For example, the fourth question on the “red” survey was

“When you think of the color red, what do you think about?” On the blue survey, the

question replaced red with blue. On the control survey, the last two questions were not

about color. As a reward, each volunteer was allowed to choose a chocolate candy in a red

wrapper or a chocolate candy in a blue wrapper. Here are segmented bar graphs showing

the results of the experiment. Describe what you see.
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