Question

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002.

      Ho:μ1=μ2Ho:μ1=μ2
      H1:μ1<μ2H1: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=14n1=14 with a mean of M1=71.4M1=71.4 and a standard deviation of SD1=7.5SD1=7.5 from the first population. You obtain a sample of size n2=12n2=12 with a mean of M2=91.1M2=91.1 and a standard deviation of SD2=20.9SD2=20.9 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 less than the second population mean.
• There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.
• The sample data support the claim that the first population mean is less than the second population mean.
• There is not sufficient sample evidence to support the claim that the first population mean is less

Answer 1

The statistical software output for this problem is:

Hence,

Critical value = -3.183

Test statistic = -3.431

Not in the critical region

Fail to reject the null

Final conclusion: Option D is correct.