29 In a recent court case it was found that during a period

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In a recent court case it was found that during a period of 11 years 862 people were selected for grand jury duty and 41% of them were from the same ethnicity. Among the people eligible for grand jury duty, 79.4% were of this ethnicity. Use a 0.05 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.

HO: p   is > or, < or, = to or, not= to 0.794?_______

H1: p   is > or, < or, = to or, not= to 0.794?_______

b. What is the test statistic? z= _______

(Round the final answer to two decimal places as needed.)

c. What is the P-value?    P-value= ________

(Round to four decimal places as needed.)

d. What is the conclusion?

A. There is sufficient evidence to support the claim.

B. There is not sufficient evidence to support the claim

e. Is the conclusion valid today? Why or why not?

A.Yes, the conclusion is valid

B.No, the conclusion is not valid

C. You can make no decisions about the validity of the conclusion

Solution

H0: p =0.794

Ha: p <0.794

One tailed test.

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z = (p^ - p₀) / ?p₀(1 - p₀) / n

Where, p^ - Observed proportion = 0.41

p₀ - Null hypothesis value = 0.794

n - sample size = 862

b) Z - test statistic = -27.877 = -27.88

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c) p value = 0.0000

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d) Conclusion: Reject null hypothesis as p <0.05.

There is sufficient evidence to support the claim.

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e) C. You can make no decisions about the validity of the conclusion

(As for current position we must determine sample size and proportion to check and conclude)