Question

In a recent court case it was found that during a period of 11 years 893 people were selected for grand jury duty and 38​% of them were from the same ethnicity. Among the people eligible for grand jury​ duty, 78.9​% 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.

Upper H 0 : p less than 0.789H0: p<0.789

Upper H 1 : p equals 0.789H1: p=0.789

B.

Upper H 0 : p not equals 0.789H0: p≠0.789

Upper H 1 : p equals 0.789H1: p=0.789

C.

Upper H 0 : p greater than 0.789H0: p>0.789

Upper H 1 : p equals 0.789H1: p=0.789

D.

Upper H 0 : p equals 0.789H0: p=0.789

Upper H 1 : p not equals 0.789H1: p≠0.789

E.

Upper H 0 : p equals 0.789H0: p=0.789

Upper H 1 : p greater than 0.789H1: p>0.789

F.

Upper H 0 : p equals 0.789H0: p=0.789

Upper H 1 : p less than 0.789

What is the test statistic?

z=? (2 decimals)

What is the p-value

P-value=? (4 decimals)

What is the conclusion on the null​ hypothesis?

RejectReject

the null hypothesis because the​ P-value is

less than or equal toless than or equal to

the significance​ level,

alphaα.

Fail to rejectFail to reject

the null hypothesis because the​ P-value is

greater thangreater than

the significance​ level,

alphaα.

Fail to rejectFail to reject

the null hypothesis because the​ P-value is

less than or equal toless than or equal to

the significance​ level,

alphaα.

RejectReject

the null hypothesis because the​ P-value is

greater thangreater than

the significance​ level,

alphaα.

Does the jury selection system appear to be​ fair?

A.There

is notis 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 notis 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.

C.There

isis

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

isis

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

for hypothesis: option F is correct: Ho: p=0.789

Ha: p <0.789

test statistic z =-29.95

p value= 0.0000

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

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.