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Chapter 11: Q. 1 (page 733)

A chi-square goodness-of-fit test is used to test whether a 0 to 9 spinner is "fair" (that is, the outcomes are all equally likely). The spinner is spun 100 times, and the results are recorded. The degrees of freedom for the test will be

(a) 8 .

(c) 10 .

(e) None of these.

(b) 9 .

(d) 99.

Short Answer

Expert verified

(b) The degrees of freedom for the test is9.

Step by step solution

01

Given Information

Need to find the degrees of freedom for the test.

02

Explanation

We have been given a 0 to 9 spinner, which has 10 possible outcomes: 0,1,2,3,4,5,6,7,8,9.

This then implies that there are 10 possible categories for the variables.

c=10

The degrees of freedom for the (chi-square goodness-of-fit) test is then the number of categories decreased by 1.

localid="1650685212354" df=c-1=10-1=9

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Most popular questions from this chapter

Aw, nuts! 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鈥檚 claim.

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

Refer to Exercises 1 and 3.

(a) Confirm that the expected counts are large enough to use a chi-square distribution. Which distribution (specify the degrees of freedom) should you use?

(b) Sketch a graph like Figure 11.4 (page 683) that shows the P-value.

(c) Use Table C to find the P-value. Then use your calculator鈥檚 C2cdf command

(d) What conclusion would you draw about the company鈥檚 claimed distribution for its deluxe mixed nuts? Justify your answer.

The appropriate null hypothesis for performing a chi-square test is that

(a) equal proportions of female and male teenagers are almost certain they will be married in 10 years.

(b) there is no difference between female and male teenagers in this sample in their distributions of opinions about marriage.

(c) there is no difference between female and male teenagers in the population in their distributions of opinions about marriage.

(d) there is no association between gender and opinion about marriage in the sample.

(e) there is no association between gender and opinion about marriage in the population.

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 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 they asked was 鈥淲hat would you most like to do at school: make good grades, be good at sports, or be popular?鈥� The two-way table below summarizes the students鈥� responses.

GoalGenderGradesPopularSportsFemale1309130Male1175060

(a) Construct an appropriate graph to compare male and female responses. Write a few sentences describing the relationship between gender and goals.

(b) Is there convincing evidence of an association between gender and goals for elementary school students? Carry out a test at the localid="1653534557186" 伪=0.05level and report your conclusion.

(c) Which cell contributes most to the chi-square statistic in part (b)? Explain

The General Social Survey asked a random sample of adults, 鈥淒o you favour or oppose the death penalty for persons convicted of murder?鈥� The following table gives the responses of people whose highest education was a high school degree and of people with a bachelor鈥檚 degree:

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) Minitab output for a chi-square test is shown below. State appropriate hypotheses and interpret the P-value in context. What conclusion would you draw? Chi-Square Test: C1, C2 Expected counts are printed below-observed counts Chi-Square contributions are printed below expected counts

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