Question

13. In a recent court case it was found that during a period of 11 years 879 people were selected for grand jury duty and 39​% of them were from the same ethnicity. Among the people eligible for grand jury​ duty, 80.2​% 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. H 0 : p < 0.802

H 1 : p = 0.802

B.H 0 : p > 0.802

H 1 : p = 0.802

C. H 0 : p = 0.802

H 1 : p > 0.802

D. H 0 : p = 0.802

    H 1 : p ≠ 0.802

E. H 0 : p ≠ 0.802

    H 1 : p = 0.802

F. H 0 : p = 0.802

H 1 : p < 0.802

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?

A.Reject the null hypothesis because the​ P-value is less than or equal to the significance​ level, alpha.

B.Fail to reject the null hypothesis because the​ P-value is less than or equal to the significance​ level, alpha.

C.Fail to reject the null hypothesis because the​ P-value is greater than the significance​ level, alpha.

D.Reject the null hypothesis because the​ P-value is greater than the significance​ level, alpha.

Does the jury selection system appear to be​ fair?

A.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.

B.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.

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 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.

Answer 1

(a)

Correct option:

H0: p = 0.802

H: p < 0.802

(b)

n = 879

p = 0.802

q = 1 - p = 0.198

SE =

Test statistic is:
Z = (0.39 - 0.802)/0.0134 = - 30.75

So

Z = - 30.75

(c)

Table of Area Under Standard Normal Curve gives area = 0.5 nearly

So,

p - value = 0.5 - 0.5 (nearly) = 0.0000

(d)

Correct option:

Reject the null hypothesis since p value is less than or equal to significance level .

(e)

Correct option:

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