Carver Memorial Hospital's surgeons have a new procedure that they think will decrease the time to perform an appendectomy. A sample of 8 appendectomies using the old method had a mean of 38 minutes with a variance of 36 minutes, while a sample of 10 appendectomies using the experimental method had a mean of 29 minutes with a variance of 16 minutes. For a right-tailed test of equal means (assume equal variances), the pooled variance is:
A)14.76
B)26.00
C)24.75
D)27.54

Question

Quizplus · Accepted Answer

To calculate the pooled variance in a two-sample t-test with equal variances, we use the formula:

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

where s1^2 and s2^2 are the sample variances of the two groups, n1 and n2 are the sample sizes of the two groups, and s_p^2 is the pooled variance.

Plugging in the given values, we get:

s_p^2 = [(8 - 1)(36) + (10 - 1)(16)] / (8 + 10 - 2) = 198 / 16 = 12.375

Therefore, the closest answer choice is C) 24.75, which is double the calculated value, and can be eliminated.

Carver Memorial Hospital's Surgeons Have a New Procedure That They