Question 1 In the Payne County medical center,a surgical director selected a random sample of 37 nurses and foundthat the mean of their ages was 39.40. The sample standarddeviation for the ages is 6.42. The director also selected a randomsample of 32 physical therapists and found the mean of their ageswas 36.77.
The sample standard deviation of ages for the physicaltherapists is 4.48.
A. [3] Give one reason why this data should not be analyzed asmatched pairs.
B. [7] Find the 99% confidence interval of the differences inthe average ages.
Group 1 is the nurses; group 2 is the physical therapists.
Assume that variances are unpooled; Satterthwaite’s formula givesDF = 64.285.
C. [3] Based on your interval, would you support or reject ahypothesis that nurses and physical therapists have the sameaverage age? Briefly explain your reasoning. [If you didn’t find aconfidence interval, use an interval from –1.11 to +6.08.]
Question 2
At the hospital, a study was done to see if there is adifference between the number of sick days taken by nurses and byphysical therapists. Since nurses deal with sicker patients, thehospital director wants to see if nurses take significantly moresick days on average, compared to physical therapists.
For the 30 nurses with at least one year of experience, the meanof the number of sick days taken was 6.47 days with sample standarddeviation s1 = 1.96. For the 22 physical therapists with data, themean was 4.76 with sample standard deviation s2 = 1.53. At the ? =0.05 level, do nurses (group 1) take significantly more sickdays?
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 topool variance for sick days.
D. [3] Make a decision and briefly explain why you made thatdecision. [If you didn’t get a test value, use 3.31.]
