Question

in a recent court case it was found that during a period of 11 years 890 people were selected for grand jury duty and 43% 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

which of the following is the hypothesis test to be conducted?

oa ( h_0:p = 0.797 )
( h_1:plt0.797 )

ob. ( h_0:p = 0.797 )
( h_1:p
eq0.797 )

oc. ( h_0:plt0.797 )
( h_1:p = 0.797 )

od. ( h_0:p = 0.797 )
( h_1:pgt0.797 )

oe ( h_0:pgt0.797 )
( h_1:p = 0.797 )

of. ( h_0:p
eq0.797 )
( h_1:p = 0.797 )

Explanation:

Step1: Identify the null and alternative hypotheses

The claim is that the selection process is biased against allowing this ethnicity to sit on the grand jury. This means we are testing if the proportion \(p\) of this ethnicity in the jury selection is less than the proportion \(p = 0.797\) of the eligible people.
The null hypothesis \(H_{0}\) is a statement of equality. The alternative hypothesis \(H_{1}\) is the claim we are testing.
So, \(H_{0}:p = 0.797\) and \(H_{1}:p<0.797\)

Answer:

A. \(H_{0}:p = 0.797\), \(H_{1}:p<0.797\)