Question

A U.S. Department of Justice Report included the claim that "in spouse murder cases, wife defendants were less likely yo be convicted than husband defendants". Sample data consisted of 277 convictions among 318 husband defendants, and 155 convictions among 222 wife defendants. Test the stated claim and identify on possible explanation for the results.

a. State the claim

b. Ho, H, c

c. Test statistic

d. Critical values

e. Conclusion and final statement

f. Construct a 95% confidence interval. Interpret the results.

Work shown in step by step and please write clearly by hand. Thanks

Answer 1

For male sample 1, we have that the sample size is N_1= 318 , the number of favorable cases is X_1 = 277 , so then the sample proportion is

For female sample 2, we have that the sample size is N_2 = 222 , the number of favorable cases is X_2 = 155 , so then the sample proportion is

The value of the pooled proportion is computed as

Also, the given significance level is α=0.05.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: p_1 = p_2

Ha: p_1 > p_2

This corresponds to a right-tailed test, for which a z-test for two population proportions needs to be conducted.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a right-tailed test is z_c = 1.64

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that z = 4.941 >zc​=1.64, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0 , and since p = 0 <0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population proportion p1​ is greater than p2​, at the 0.05 significance level.

The critical value for α=0.05 is z_c ​=1.96. The corresponding confidence interval is computed as shown below:

CI = (0.102, 0.244)