Question

A sample of 38 observations is selected from a normal population. The sample mean is 47, and the population standard deviation is 7. Conduct the following test of hypothesis using the 0.05 significance level.

The value of the test statistic is -.88

the decision rule is Reject H₀ if z < −1.960 or z > 1.960

1. e-1. What is the p-value? (Round your z value to 2 decimal places and final answer to 4 decimal places.)

1. e-2. Interpret the p-value? (Round your z value to 2 decimal places and final answer to 2 decimal places.)

there is a _____ % chance of finding a z value this large by "sampling error" when H0 is true.

Answer 1

a) As we are given here the rejection region as:
Reject H₀ if z < −1.960 or z > 1.960

Therefore this is a two tailed test here. The p-value therefore is computed here as:
p = 2 P(Z < -0.88)

Getting it from the standard normal tables, we have here:
p = 2 P(Z < -0.88) = 2*0.1894 = 0.3788

Therefore 0.3788 is the required p-value here.

b) The interpretation of the p-value of 0.3788 is that there is a 0.3788 probability of getting the required sample results given that the null hypothesis is true. Therefore there is a 37.88% chance of finding a z value this large by sampling error when H0 is true.