Question

Question 1 In the Payne County medical center, a surgical director selected a random sample of 37 nurses and found that the mean of their ages was 39.40. The sample standard deviation for the ages is 6.42. The director also selected a random sample of 32 physical therapists and found the mean of their ages was 36.77.

The sample standard deviation of ages for the physical therapists is 4.48.

A. [3] Give one reason why this data should not be analyzed as matched pairs.

B. [7] Find the 99% confidence interval of the differences in the average ages.
Group 1 is the nurses; group 2 is the physical therapists.
Assume that variances are unpooled; Satterthwaite’s formula gives DF = 64.285.

C. [3] Based on your interval, would you support or reject a hypothesis that nurses and physical therapists have the same average age? Briefly explain your reasoning. [If you didn’t find a confidence interval, use an interval from –1.11 to +6.08.]

Question 2

At the hospital, a study was done to see if there is a difference between the number of sick days taken by nurses and by physical therapists. Since nurses deal with sicker patients, the hospital director wants to see if nurses take significantly more sick days on average, compared to physical therapists.

For the 30 nurses with at least one year of experience, the mean of the number of sick days taken was 6.47 days with sample standard deviation s1 = 1.96. For the 22 physical therapists with data, the mean was 4.76 with sample standard deviation s2 = 1.53. At the α = 0.05 level, do nurses (group 1) take significantly more sick days?

A. [3 points] What are the null and alternative hypotheses? H0: H1:
B. [3] What is the rejection region for this test?

C. [5] Compute the test value. Hospital statisticians decide to pool variance for sick days.

D. [3] Make a decision and briefly explain why you made that decision. [If you didn’t get a test value, use 3.31.]

Answer 1