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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-p20

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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