Question

You wish to test the following claim ( H a ) at a significance level of α = 0.02 . H o : μ 1 = μ 2 H a : μ 1 ≠ μ 2 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 the following two samples of data. 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 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.

Sample #1

Sample #2

39.6	47.3	21.2
16.3	34.1	43.8
95.6	52.9	90.1
35.2	67.4	59.8
44.4	59.8	57.5
30.3	63.9	70
59.8

49.6	62.6	45.1
70.3	53.9	57.6
49.9	33.4	45.9
43.5

Answer 1

we have null and alternate hypothesis

H o : μ 1 = μ 2

H a : μ 1 ≠ μ 2

using minitab

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 19 52.1 20.9 4.8
sample 2 10 51.2 10.5 3.3

Difference = μ (sample 1) - μ (sample 2)
Estimate for difference: 0.87
98% CI for difference: (-16.62, 18.37)
T-Test of difference = 0 (vs ≠): T-Value = 0.122 P-Value = 0.903 DF = 27
Both use Pooled StDev = 18.1098

the critical value for this test =±2.473

the test statistic for this sample = 0.122

since 0.122 < 2.473

The test statistic is in the critical region This test statistic leads to a decision to fail to reject the null hypothesis

here is sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean.