Question

In: Math

A rehabilitation center researcher was interested in examining the relationship between physical fitness prior to surgery...

A rehabilitation center researcher was interested in examining the relationship between physical fitness prior to surgery of persons undergoing corrective knee surgery and time required in physical therapy until successful rehabilitation. Patient records in the rehabilitation center were examined, and 24 male subjects ranging in age from 18 to 30 years 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.

j

i

1

2

3

4

5

6

7

8

9

10

1

Below Average

29

42

38

40

43

40

30

42

2

Average

30

35

39

28

31

31

29

35

29

33

3

Above Average

26

32

21

20

23

22

  1. Explore the with side-by-side box-plots. Discuss the results of your graphical exploration.
  2. Calculate group mean and standard deviation.
  3. Complete a one-way analysis of variance for this problem. Show all hypothesis-testing steps and interpret the results.

Solutions

Expert Solution

Using Minitab:

a.

The boxplot for the data shows that Below Average has both the highest median and variability

Average and above average  appear to have roughly similar variability.

Part b.

Part c.

The p-value for the paint hardness ANOVA is 0.000. Thus, assuming you chose the commonly used a-level of 0.05 for the test, you would conclude that there are significant differences in physical therapy and the prior physical fitness status.


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