Question

in a recent court case it was found that during a period of 11 years 897 people were selected for grand jury duty and 42% of them were from the same ethnicity. among the people eligible for grand jury duty, 80.7% 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. $h_{0}:p = 0.807$ $h_{1}:p
eq0.807$ b. $h_{0}:p
eq0.807$ $h_{1}:p = 0.807$ c. $h_{0}:p>0.807$ $h_{1}:p = 0.807$ d. $h_{0}:p = 0.807$ $h_{1}:p>0.807$ e. $h_{0}:p<0.807$ $h_{1}:p = 0.807$ f. $h_{0}:p = 0.807$ $h_{1}:p<0.807$

Explanation:

Step1: Understand the claim

The claim is that the selection process is biased against allowing this ethnicity to sit on the grand jury. That means the proportion \(p\) of this ethnicity in the grand - jury selection is less than the proportion \(0.807\) of this ethnicity among eligible people.

Step2: Formulate the hypotheses

The null hypothesis \(H_0\) is a statement of equality. The alternative hypothesis \(H_1\) is the claim we are trying to find evidence for.
For a claim of \(p < 0.807\), the null hypothesis \(H_0:p = 0.807\) (assuming no bias) and the alternative hypothesis \(H_1:p<0.807\)

Answer:

F. \(H_0:p = 0.807\), \(H_1:p < 0.807\)