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Chapter 11: Q. 44 (page 726)

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).

Short Answer

Expert verified

(a) H0: There is no association between the variables

Ha: There is an association between the variables

If there is no association between the variables, then we have a probability of 0.0%of obtaining a similar or more extreme sample.

(b) We can deduce from this P-value that there is a difference between the population proportions, which is the case if the variables are related.

As a result, the two-sample z-test and the chi-square test are equivalent, as seen by the similar P-values.

Step by step solution

01

Part (a) Step 1: Given information

The given data is

02

Part (a) Step 2: Explanation

The null hypothesis states that there is no association between the variables:

H0: There is no association between the variables

(type of degree and favoring death penalty)

The alternative hypothesis states that there is an association between the variables:

Ha: There is an association between the variables

(type of degree and favoring death penalty)

The p-value is given as

P=0.000=0.0%

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme if the null hypothesis is true.

If there is no association between the variables, then we have a probability of 0.0%obtaining a similar or more extreme sample.

H0: There is no association between the variables

Ha: There is an association between the variables.

03

Part (b) Step 1: Given information

The given data is

04

Part (b) Step 2: Explanation

Find the hypothesis

H0:p1-p2=0

H0:p1-p2鈮�0

The P- value is

P=0.000=0.0%

We can deduce from this P-value that there is a difference between the population proportions, which is the case if the variables are related.

As a result, the two-sample z-test and the chi-square test are equivalent, as seen by the similar P-values.

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Most popular questions from this chapter

The P-value for a chi-square goodness-of-fit test is 0.0129. The correct conclusion is

(a) reject H0at 伪=0.05; there is strong evidence that the trees are randomly distributed.

(b) reject H0at 伪=0.05; there is not strong evidence that the trees are randomly distributed.

(c) reject H0at 伪=0.05; there is strong evidence that the trees are not randomly distributed.

(d) fail to reject H0at 伪=0.05; there is not strong evidence that the trees are randomly distributed.

(e) fail to reject H0at 伪=0.05; there is strong evidence that the trees are randomly distributed.

Refer to Exercises 2 and 4.

(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 whether the roulette wheel is operating correctly? Justify your answer

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

(a) How do opinions about banning handgun ownership seem to be related to the level of education? Make an appropriate graph to display this relationship. Describe what you see.

(b) Determine whether or not the sample provides convincing evidence that education level and opinion about a handgun ban are independent in the adult population

Refer to Exercise 27. Do the data provide convincing evidence of a difference in the distributions of sports goals for male and female undergraduates at the university?

(a) State appropriate null and alternative hypotheses for a significance test to help answer this question.

(b) Calculate the expected counts. Show your work.

(c) Calculate the chi-square statistic. Show your work

From exercise27

Why men and women play sports Do men and women participate in sports for the same reasons? One goal for sports participants is social comparision鈥攖he desire to win or to do better than other people. Another is mastery鈥攖he desire to improve one鈥檚 skills or to try one鈥檚 best. A study on why students participate in sports collected data from independent random samples of 67 male and 67 female under-graduates at a large university 15 Each student was classified into one of four categories based on his or her responses to a questionnaire about sports goals. The four categories were high social comparison鈥� high mastery (HSC-HM), high social comparison鈥� low mastery (HSC-LM), low social comparison鈥揾igh mastery (LSC-HM), and low social comparison鈥搇ow mastery (LSC-LM). One purpose of the study was to compare the goals of male and female students. Here are the data displayed in a two-way table: Observed Counts for Sports Goals

(a) Check that the conditions for performing the chi-square test are met.

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

(c) Interpret the P-value from the calculator in context.

(d) What conclusion would you draw? Justify your answer.
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