Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 20 men employed by a medium-sized company. The women took an average
Of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men took an average of 20.5 hours of personal time per year with a standard deviation of 2.75 hours. If we use the pooled t-test to see if there is a difference between the two groups,the degrees of freedom for the appropriate t-statistic is
A) 36
B) 34
C) 20
D) 16
E) None of the above.

Question

Quizplus · Accepted Answer

To calculate the degrees of freedom for the pooled t-test, we use the formula:

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

Plugging in the values from the problem, we get:

df = ((2.84^2/16) + (2.75^2/20))^2 / [((2.84^2/16)^2 / (16 - 1)) + ((2.75^2/20)^2 / (20 - 1))] 
   = (0.399 + 0.381)^2 / (0.035 + 0.033)
   = 0.78^2 / 0.068
   = 9.14

Rounding down to the nearest integer, we get df = 9. Therefore, the answer is B) 34.

Data Were Collected on Annual Personal Time (In Hours) Taken