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Chapter 11: Q. 45 (page 755)

Tuition bills A random sample of U.S. adults was recently asked, 鈥淲ould you support or oppose major new spending by the federal government that would help undergraduates pay tuition at public colleges without needing loans?鈥� The two-way table shows the responses, grouped by age.

Do these data provide convincing evidence of an association between age and opinion about loan-free tuition in the population of U.S. adults?

Short Answer

Expert verified

Yes, these data provide convincing evidence of an association between age and opinion about loan-free tuition in the population of U.S. adults.

Step by step solution

01

 Step 1: Given information 

We havew to tell about convincing evidence of an association between age and opinion about loan-free tuition in the population of U.S. adults.

02

Explanation 

The significamce level of 伪is 0.05.

The age of the respondent has no bearing on the response.

The expected frequencies are:

E11=r1脳c1n=856脳1201509鈮�68.07

Finally, after determining all of the other characteristics, we arrive at

E34=r3脳c4n=88脳6381509鈮�37.21

Hypothesis Test:

蠂2=鈭�(O-E)2E

Using the above formula we get =39.74

P<0.05鈬�RejectH0

There is evidence to suggest that there is a link between age and response.

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Most popular questions from this chapter

Recent revenue shortfalls in a midwestern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 25%tuition increase. It was determined that such an increase was needed simply to compensate for the lost support from the state. Separate random samples of 50freshmen, 50sophomores, 50juniors, and 50seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. Here are the results:

Which null hypothesis would be appropriate for performing a chi-square test?

a. The closer students get to graduation, the less likely they are to be opposed to tuition increases.

b. The mean number of students who are strongly opposed is the same for each of the 4years.

c. The distribution of student opinion about the proposed tuition increase is the same for each of the 4years at this university.

d. Year in school and student opinion about the tuition increase are independent in the sample.

e. There is an association between year in school and opinion about the tuition increase at this university.

Which of the following statements about chi-square distributions are true?

I. For all chi-square distributions, P(x2鈮�0)=1

II. A chi-square distribution with fewer than 10degrees of freedom is roughly symmetric.

III. The more degrees of freedom a chi-square distribution has, the larger the mean of the distribution.

a. I only

b. II only

c. III only

d. I and III

e. I, II, and III

How far away do you live? Conduct a follow-up analysis for the test in Exercise50.

Where do young adults live? A survey by the National Institutes of Health asked a random sample of young adults (aged 19to 25years), 鈥淲here do you live now? That is, where do you stay most often?鈥� 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?

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?
See all solutions

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