Question

Hypothesis Test for the Difference in Population Means (σσ  Unknown)

You wish to test the following claim (HaHa) at a significance level of α=0.005α=0.005.

      Ho:μ1=μ2Ho:μ1=μ2
      Ha:μ1>μ2Ha:μ1>μ2

You believe both populations are normally distributed, but you do not know the standard deviations for either. Let's assume that the variances of the two populations are not equal. You obtain the following two samples of data.

Sample #1

60	62.8	60.2
48.5	61.8	52.7
65.1	66.3	71.4
72.2	63.8	59.5
70.5	58.3	79.6
57.4

Sample #2

76.7	75.2	71.3
38.7	75.2	86.9
57.3	47.7	25.9
74.4	52.6

What is the test statistic for this sample? (Keep sample statistics rounded to 3 decimal places. Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

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.

License

Answer 1

The statistical software output for this problem is :

Test statistics = 0.189

P-value = 0.4265

The p-value is greater than α .

fail to reject the null .

There is not sufficient sample evidence to support the claim that the first population

mean is greater than the second population mean.