Question

You wish to test the following claim (H1) at a significance level of α=0.01

      Ho:μ1=μ2
      H1:μ1>μ2

You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n1=20 with a mean of M1=84.6 and a standard deviation of SD1=18.1 from the first population. You obtain a sample of size n2=21 with a mean of M2=75 and a standard deviation of SD2=8.3 from the second population.

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

Answer 1

The statistical software output for this problem is :

critical value = 2.479

Test statistics = 2.165

The test statistic is not in the critical region .

fail to reject the null

There is not sufficient evidence to warrant rejection of the claim that the first population mean is greater than the second population mean.