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, 79.7​% 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.

Answer 1

From the given data,

Here,

sample size = n = 881

sample proportion p^ = 0.41

Null hypothesis Ho : p = 0.797

Alternative hypothesis Ha : p != 0.797

Here at 0.05 significance level , z critical value = +/- 1.96

test statistic z = (p^ - p) / sqrt(pq/n)

substitute values

= (0.41 - 0.797) / sqrt(0.797(1-0.797)/881)

z = - 28.56

Here it is two tailed test, the corresponding p value for z = -28.56 is 0.

Here p value < alpha.

So we reject Ho.

So there is enough evidence to claim that the selection process is biased against allowing this ethnicity to sit on the grand jury.

Thank you.