In a study, a random sample of 34 male college students ran one mile while another random sample of 38 male college students walked the same mile. On average, those who ran burned 112 calories while those who walked burned 89 calories. Determine the degrees of freedom for a hypothesis test for the difference between the two population means for population variances assumed unequal (nonpooled estimate of the standard deviation) to test whether running burns more calories than walking.

To determine the degrees of freedom for a hypothesis test comparing the means of two populations with unequal variances, we use the Welch-Satterthwaite formula. This formula takes into account the sample sizes and variances of the two groups.

In this case, we have a sample of 34 male college students who ran and another sample of 38 male college students who walked. The sample mean and sample variance for the running group are 112 calories and an unknown variance denoted as s1^2. The sample mean and sample variance for the walking group are 89 calories and an unknown variance denoted as s2^2.

The degrees of freedom for this test can be calculated using the following formula:

df = (s1^2/n1 + s2^2/n2)^2 / [(s1^2/n1)^2 / (n1-1) + (s2^2/n2)^2 / (n2-1)]

Substituting the values into the formula, we have:

n1 = 34 (sample size of the running group)

n2 = 38 (sample size of the walking group)

Since we do not have the actual sample variances, we cannot determine the exact degrees of freedom without additional information.

However, using the formula above, you can substitute the actual values of s1^2 and s2^2 (the sample variances) to calculate the degrees of freedom for your specific data.