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.

c. ( h_{0}:p>0.807 )
( h_{1}:p = 0.807 )
e. ( h_{0}:p<0.807 )
( h_{1}:p = 0.807 )
d. ( h_{0}:p = 0.807 )
( h_{1}:p>0.807 )
f. ( h_{0}:p = 0.807 )
( h_{1}:p<0.807 )
what is the test statistic?
( z=-29.37 )
(round to two decimal places as needed.)
what is the p - value?
( p - value = 0.000 )
(round to three decimal places as needed.)
what is the conclusion on the null hypothesis?
reject the null hypothesis because the p - value is greater than the significance level, ( alpha ).
reject the null hypothesis because the p - value is less than or equal to the significance level, ( alpha ).
fail to reject the null hypothesis because the p - value is less than or equal to the significance level, ( alpha ).
fail to reject the null hypothesis because the p - value is greater than the significance level, ( alpha ).

Explanation:

Step1: Recall the decision rule for hypothesis testing

If \(P - value\leq\alpha\), we reject \(H_0\). Here, \(\alpha = 0.01\) and \(P - value=0.000\).
Since \(0.000\leq0.01\) (i.e., \(P - value\leq\alpha\))

Answer:

Reject the null hypothesis because the \(P\) - value is less than or equal to the significance level, \(\alpha\).