In order to test the difference between the population means, the test statistic is t-distributed with 38 degree of freedom
The first independent sample of size = 15
The second independent sample of size = 25
Randomly selected from two normal populations with equal variances
The degree of freedom = The first independent sample of size + The second independent sample of size - 2
Substitute the values in the equation of degree of freedom
The degree of freedom = 15 + 25 - 2
Add the terms
= 40 - 2
Subtract the numbers
= 38
Therefore, the test statistic is t-distributed with 38 degree of freedom
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