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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

More candy The two-way table shows the results of the experiment

described in Exercise 27.


Red SurveyBlue Survey
Control Survey
Total
Red Candy13
5
8
26
Blue Candy
7
15
12
34
Total20
20
20
60

a. State the appropriate null and alternative hypotheses.

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

complete table of expected counts.

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

Regulating guns The National Gun Policy Survey asked a random sample of adults, "Do you think there should be a law that would ban possession of handguns except for the police and other authorized persons?" Here are the responses, broken down by the respondent's level of education:

Do these data provide convincing evidence at the 伪=0.05level of an association between education level and opinion about a handgun ban in the adult population?

Preventing strokes Aspirin prevents blood from clotting and so helps prevent strokes.

The Second European Stroke Prevention Study asked whether adding another anticlotting

drug named dipyridamole would be more effective for patients who had already had a

stroke. Here are the data on strokes during the two years of the study

a. Summarize these data in a two-way table.

b. Do the data provide convincing evidence of a difference in the effectiveness of the four

treatments at the伪=0.05significance level?

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.

Video games (1.1) To determine if there is a relationship between age and playing video games, the Pew Research Center asked randomly selected adults for their age and if they 鈥渆ver play video games on a computer, TV, game console, or portable device like a cell phone.鈥�3 Here is a two-way table summarizing the results of the study:

a. Construct a segmented bar graph to display the relationship between age group and response to the question about video games.

b. Describe the association shown in the segmented bar graph in part (a).
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