You wish to test the following claim (Ha) at a significancelevel of α=0.002.

      Ho:μ1=μ2 Ha:μ1<μ2

You believe both populations are normally distributed, but you donot know the standard deviations for either. However, you also haveno reason to believe the variances of the two populations are notequal. You obtain a sample of size n1=18 with a mean of M1=59.3 anda standard deviation of SD1=15.2 from the first population. Youobtain a sample of size n2=13 with a mean of M2=69.1 and a standarddeviation of SD2=5.7 from the second population.

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

What is the test statistic for this sample? (Report answer accurateto 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 claimthat the first population mean is less than the second populationmean.
• There is not sufficient evidence to warrant rejection of theclaim that the first population mean is less than the secondpopulation mean.
• The sample data support the claim that the first populationmean is less than the second population mean.
• There is not sufficient sample evidence to support the claimthat the first population mean is less than the second populationmean.

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