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. $h_0:p = 0.807$
$h_1:p<0.807$
what is the test statistic?
$z=-29.37$
(round to two decimal places as needed.)
what is the p - value?
$p - value=square$
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the P - value

Since the test is a left - tailed test (because \(H_1:p < 0.807\)) and the test statistic \(z=-29.37\).
The P - value for a left - tailed test is \(P(Z<z)\).
For a standard normal distribution \(Z\), when \(z=-29.37\), using the property of the standard normal distribution (the area under the curve for \(Z < - 3.49\) is approximately \(0.0003\) and for very large negative \(z\) values, the area approaches \(0\)).
\(P - value\approx0.000\)

Answer:

\(P - value = 0.000\)