Question

Assume that the significance level is α=0.05. Use the given information to find the​ P-value and the critical​ value(s).With H₁: p≠23​, the test statistic is z=−1.79.

a. ​P-value=.____

b. The critical​ value(s) is/are _____.

Answer 1

It is given that alternative hypothesis is two-tailed.That is :H₁: p≠23​

Given test statistic is: z= -1.79

Now,The p- value can be calculated as:

2P(Z > |z|)=2P(Z > |-1.79|)

=2*[1-P(z<1.79)]  

=2*[1-0.9633] [ From Standard normal Z table P(z<1.79)=0.9633]

=0.0734

Thus,P-value =0.0734

Since,Given level of significance =α=0.05

Thus,The critical value can be calculated using the Excel command as:=NORMINV(1-0.05/2,0,1)

The critical value = 1.96