A rehabilitation center researcher is interested in examining the relationship between physical fitness prior to surgery of persons undergoing corrective knee surgery and the time required in physical therapy until successful rehabilitation. Patient records in the rehabilitation center were examined, and 30 male subjects ranging in age from 18 to 30 years (10 in each group), who had undergone similar corrective knee surgery during the past year were selected for the study. The number of days required for successful completion of physical therapy and the prior physical fitness status (below average, average, above average) for each patient follow:
|
Patient
|
|
Group
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
Below average
|
29
|
42
|
38
|
40
|
43
|
40
|
30
|
42
|
41
|
40
|
|
Average
|
30
|
35
|
39
|
28
|
31
|
31
|
29
|
35
|
29
|
33
|
|
26
|
32
|
21
|
20
|
23
|
22
|
21
|
24
|
20
|
22
|
|
a) Is the mean number of days required for successful completion of physical therapy equal for all the three groups? Test at a chosen level of significance of 1%.
b) If the null hypothesis in part a) is rejected, determine on a pair-wise basis, which groups have a different mean number of days required for successful completion of physical therapy. Use a family significance level of 5%. Discuss your conclusions.
c) Find a 98% confidence interval for the mean number of days required for successful completion of physical therapy for patients in the average group. Discuss the results.