Question

In a recent court case it was found that during a period of 11 years 872 people were selected for grand jury duty and 42 % of them were from the same ethnicity. Among the people eligible for grand jury duty, 80.5% were of this ethnicity. Use a 0.01 significance level to test the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution. Which of the following is the hypothesis test to be conducted? A. H0: p < 0.805 H1: p = 0.805 B. H0: p = 0.805 H1: p ≠ 0.805 C. H0: p = 0.805 H1: p < 0.805 D. H0: p > 0.805 H1: p = 0.805 E. H0: p = 0.805 H1: p > 0.805 F. H0: p ≠ 0.805 H1: p = 0.805 What is the test statistic? z = (Round to two decimal places as needed.) What is the P-value? P-value = (Round to four decimal places as needed.) What is the conclusion on the null hypothesis? i) Reject the null hypothesis because the P-value is less than or equal to the significance level, α. ii) Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, α. iii) Reject the null hypothesis because the P-value is greater than the significance level, α. iv) Fail to reject the null hypothesis because the P-value is greater than the significance level, α. Does the jury selection system appear to be fair? A. There is not sufficient evidence to warrant rejection of the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. The jury selection process appears to be fair. B. There is not sufficient evidence to support the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. The jury selection process appears to be unfair. is not C. There is sufficient evidence to warrant rejection of the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. The jury selection process appears to be fair. D. There is sufficient evidence to support the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. The jury selection process appears to be unfair.

Answer 1

Solution:

Sample proportion = = 0.42

Sample size = n = 872

Level of significance = 0.01

Null and alternative hypothesis:

This corresponding to a two-tailed test, for which a z-test for one population proportion needs to be used.

Test statistic:

P-value: Using excel function, =NORMSDIST(-28.69)

P-value = 0

Since, P-value < 0.01

Decision: Reject the null hypothesis because the P-value is less than or equal to the significance level, α.

Conclusion: There is sufficient evidence to support the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. The jury selection process appears to be unfair.

Done