Question

You wish to test the following claim (H1H1) at a significance level of α=0.02α=0.02.

      Ho:μ1=μ2Ho:μ1=μ2
      H1:μ1>μ2H1:μ1>μ2

You obtain the following two samples of data.

Sample #1	Sample #2
97.7 78.7 14.7 91.3 90.1 39.8 56.9 47.2 67.5 62.3 64.9 26.7 79.4 52.9 63.3 69.1 20.4 67.5 54.1 67 46.4 52.3 44.2 65.9 95.8 56.9 78.7 85.9 56.4 59.1 53.5 72.5 70.8 61.2 64.9 70.2 68.6 44.2 41.6 77.4 81.6 14.7 55.2 71.4 56.4 50.5 52.9 41.6 24 49.9 53.5 74.9 56.4 38.7 70.8 37.7 88.9 37.7 45 59.6	43.9 77.9 24.6 28.5 32.7 66.7 36 62.1 63.1 36.9 47.6 64.6 76.4 80.4 49.3 55.1 88.2 22 41.1 22 96.2 26.7 67.8 57.6 46.4 93.6 91.5 13.3 70 41.1 44.5 73.7 91.5 79.5 99.6 55.6 26.7 74.3 69.4 70.6 13.3 51.5 72.4 86.8 49.9 99.6 86.8 45.2 49.9 52.6 47 69.4

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? (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.

Answer 1

we have given

a significance level of α=0.02

      Ho:μ1=μ2
      H1:μ1>μ2

using minitab>stat>basic stat>2 sample t

we have

Two-Sample T-Test and CI: sample 1, sample 2

Two-sample T for sample 1 vs sample 2

N Mean StDev SE Mean
sample 1 60 59.0 19.0 2.5
sample 2 52 58.3 23.5 3.3

Difference = μ (sample 1) - μ (sample 2)
Estimate for difference: 0.66
98% lower bound for difference: -7.69
T-Test of difference = 0 (vs >): T-Value = 0.165 P-Value = 0.4348 DF = 110

the test statistic for this sample
test statistic =0.165

the p-value for this sample
p-value =0.4348

The p-value is. greater than α

This test statistic leads to a decision to fail to reject the null

As such, the final conclusion is that...

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