Question

In a recent court case it was found that during a period of 11 years

881

people were selected for grand jury duty and

41​%

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.

H0: p=0.802

H1: p<0.802

Your answer is correct.

B.

H0: p=0.802

H1: p>0.802

C.

H0: p<0.802

H1: p=0.802

D.

H0: p=0.802

H1: p≠0.802

E.

H0: p>0.802

H1: p=0.802

F.

H0: p≠0.802

H1: p=0.802

What is the test​ statistic?

z=negative 29.13−29.13

​(Round to two decimal places as​ needed.)

What is the​ P-value?

Answer 1

using excel>addin>phstat>one sample test

we have

.

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.802
Level of Significance	0.05
Number of Items of Interest	361
Sample Size	881
Intermediate Calculations
Sample Proportion	0.41
Standard Error	0.0134
Z Test Statistic	-29.1981
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0000
Reject the null hypothesis
Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.802
Level of Significance	0.05
Number of Items of Interest	361
Sample Size	881
Intermediate Calculations
Sample Proportion	0.41
Standard Error	0.0134
Z Test Statistic	-29.1981
Two-Tail Test
Lower Critical Value	-2.5758
Upper Critical Value	2.5758
P value	0.0000
Reject the null hypothesis

the null and alternative hypothesis is

D.H0: p=0.802

H1: p≠0.802

z test stat = -29.20

p value= 0.000

there is sufficient evidence to support the claim the selection process is biased against allowing this ethnicity to sit on the grand jury