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.

H0: μ =48

H1: μ ≠ 48

What is the decision rule?

Reject H0 if z < -1.960 or z > 1.960

A.) What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

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

C.) Interpret the p-value? (Round 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

The null hypothesis is,

against the alternative hypothesis,

This is two tailed test.

Given that,

sample size,

sample mean,

population standard deviation,

level of significance,

The test statistic will be computed as:

The p-value for the two tailed Z test corresponds to the probability which can be obtained using the Excel function NORMSDIST(z) as below:

                                

                                

Now, it can be observed that the p-value = 0.3785 is not less than the level of signifcance, , thus, we cannot reject the null hypothesis.

And hence it is concluded that, μ = 48 .