Question

We test for a hypothesized difference between two population means: H0: µ1 = µ2. The population standard deviations are unknown but assumed equal. The number of observations in the first sample is 15 and 12 in the second sample. How many degrees of freedom are associated with the critical value?

A. 24
B. 25
C. 26
D. 27

Answer 1

The degrees of freedom associated with the critical value for a t-test with 15 observations in the first sample and 12 in the second sample, both with unknown but assumed equal population standard deviations, is 27.

Step-by-step explanation:

The question relates to the calculation of degrees of freedom (df) in the context of a hypothesis test comparing two population means, where the population standard deviations are unknown and assumed to be equal. The t-distribution will be used since the standard deviations are unknown and the sample sizes are smaller than 30. The formula for the degrees of freedom in a two-sample t-test with equal variances is df = n1 + n2 - 2. In this case, n1, the number of observations in the first sample, is 15, and n2, the number of observations in the second sample, is 12. So, the degrees of freedom would be calculated as df = 15 + 12 - 2 = 27.