You wish to test the following claim (HaHa) at a significance level of =0.02=0.0

Question

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

      Ho:1=2
      Ha:12

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? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to three decimal places.)
critical value = ±

For critical value, I tried 2.421, 2.429, 2.428, 2.418, 2.792, 2.746, 2.552, but none of them were right.

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

Sample #1 Sample #2 79.1 64.6 57.5 69.9 82 79.1 62.4 88.2 57.5 51.6 55.7 73.1 56.9 77.3 80.5 77.7 64.6 92.6 86.1 100.2 64.2 60.6 44.1 54.5 100.2 92.9 68.9 76.8 85.1 99.3 87.8 114.9 80.8 95.4 69.9 94.9 75.3 87.4 86.6 81.2 79 87.8 65.9 55.2

Explanation / Answer

The statistical software output for this problem is:

Two sample T hypothesis test:
1 : Mean of Sample #1
2 : Mean of Sample #2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 0
(with pooled variances)

Hypothesis test results:

Hence,

Degrees of freedom = 42

So,

Critical value for a two tailed test with 42 degrees of freedom and = 0.02 will be:

Critical value = ± 2.418

Its coming 2.418 only which you already tried. May be trying 2.419 would help. I am not sure why the system is not taking 2.418 as a correct answer. [Please try 2.419 and check if its correct]

Test statistic = -2.755

Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 -12.218316 4.435619 42 -2.7545909 0.0086

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