Question

You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01.

      Ho:μ=72.8Ho:μ=72.8
      Ha:μ>72.8Ha:μ>72.8

You believe the population is normally distributed and you know the standard deviation is σ=5.8σ=5.8. You obtain a sample mean of M=74.8M=74.8 for a sample of size n=46n=46.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

• in the critical region
• not in the critical region

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 72.8.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 72.8.
• The sample data support the claim that the population mean is greater than 72.8.
• There is not sufficient sample evidence to support the claim that the population mean is greater than 72.8.

Answer 1

Given: n=46

M=74

At 1% level of significance we want to test the hypothesis that:

Z critical value at 1% level of significance for upper tail test is:

The test statistic is:

## Since population standard is known we used z test.

The test statistic is not in the critical region.

Since , we are unable to reject the null hypothesis.

Conclusion:

• There is not sufficient sample evidence to support the claim that the population mean is greater than 72.8.