Question

You wish to test the following claim (Ha) at a significance level of α=0.02.

      Ho: μ1 = μ2
      Ha: μ1 ≠ μ2

You obtain the following two samples of data.

Sample #1

Sample #2

85.1	56.6	74.4	72
72.8	77.6	76.4	70.2
54.5	76.9	65.6	54.5
67.2	86.9	84.4	68.4
73.2	74.8	80.7	70.4
76	74.2	86.9	83.8
54.5	67.4	60.4	63
72.4	85.9	78.9	85.9
69	68.4	64.1	73.6
67	68.8	59.7	85.9

58.6	71.4	57.6	72.6
73.9	83.1	79.1	67.4
61	63.7	85.1	72.9
57.6	74.6	79.4	67.1
66.8	76.1	74.1	78.6
80	71.6	76.3	58.6
67.7	58.6	77.6	65.3
56.4	70.3	81.5	73.9
73.4	64.5	85.5	83.9
64.1	81.5	64.1

What is the test statistic for this sample? (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 not equal to the second population mean.
• There is not sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean.
• The sample data support the claim that the first population mean is not equal to the second population mean.
• There is not sufficient sample evidence to support the claim that the first population mean is not equal to the second population mean.

Answer 1

The statistical software output for this problem is:

On the basis of above output:

Test statistic = 0.515

P - value = 0.6079

greater than α

Fail to reject the null

There is not sufficient sample evidence to support the claim that the first population mean is not equal to the second population mean.