Question

In a recent court case it was found that during a period of 11 years 861people were selected for grand jury duty and 38​% of them were from the same ethnicity. Among the people eligible for grand jury​ duty, 78.3​% were of this ethnicity. Use a 0.01significance 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

null Hypothesis:               Ho:   p		=	0.783
alternate Hypothesis:    Ha: p		<	0.783

sample success x   =		327
sample size          n    =		861
std error   se =√(p*(1-p)/n) =		0.0140
sample proportion p̂ = x/n=		0.3800
test stat z =(p̂-p)/√(p(1-p)/n)=		-28.69
p value                          =		0.0000

since p value <0.01 , we reject null hypothesis and conclude that representation is less than 78.3% or  support the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury