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 means (assume equal variances), the test statistic is:
A)3.814
B)2.365
C)3.000
D)1.895

Question

Quizplus · Accepted Answer

To test whether the new procedure decreases the time to perform an appendectomy, we can use a two-sample t-test for the difference in means. Since the sample variances are given, we can use a pooled variance estimate:

s_p = sqrt(((n1-1)*s1^2 + (n2-1)*s2^2)/(n1+n2-2))

Plugging in the values, we get:

s_p = sqrt(((8-1)*36 + (10-1)*16)/(8+10-2))
s_p = 5.123

The test statistic is then:

t = (x1bar - x2bar) / (s_p * sqrt(1/n1 + 1/n2))

Plugging in the values, we get:

t = (38 - 29) / (5.123 * sqrt(1/8 + 1/10))
t = 3.814

Since we are conducting a right-tailed test, the critical value for alpha = 0.05 and degrees of freedom = 16 is 1.746, which is less than our test statistic of 3.814. Therefore, we reject the null hypothesis and conclude that the new procedure significantly decreases the time to perform an appendectomy.

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