A jury list contains the names of all individuals who may be

A jury list contains the names of all individuals who may be called for jury duty. The proportion of the available jurors on the list who are women is 0.53. If 40 people are selected to serve as candidates for being picked on the jury, show all the steps of a significance test of the hypothesis that the selections are random with respect to gender. NEATLY number and clearly display all eight steps of hypothesis testing

a. set up notation and hypothesis, and specify assumptions.

b. 5 of the 40 selected were women. FInd the test statistic.

c. Report the p- value and interpret.

d. explain how to make a decision using a significance level of 0.01.

Solution

Set Up Hypothesis
Null, H0:P=0.53
Alternate,the selections are random with respect to gender H1: P!=0.53
Test Statistic
No. Of Success chances Observed (x)=5
Number of objects in a sample provided(n)=40
No. Of Success Rate ( P )= x/n = 0.125
Success Probability ( Po )=0.53
Failure Probability ( Qo) = 0.47
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.125-0.53/(Sqrt(0.2491)/40)
Zo =-5.1321
| Zo | =5.1321
Critical Value
The Value of |Z | at LOS 0.01% is 2.58
We got |Zo| =5.132 & | Z | =2.58
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -5.13214 ) = 0
Hence Value of P0.01 > 0,Here we Reject Ho

We have the evidence to indicate that selections are random with respect to gender