### 1D 1 A Rehabilitation Center Researcher Was

##### Question

# 1(d) 1. A rehabilitation center researcher was interested in e amining the relationship between physical fitness priort surgery and the time (in days) for successful completion physical therapy….

1. A rehabilitation center researcher was interested in e amining the relationship between physical fitness priort surgery and the time (in days) for successful completion physical therapy. The fitness levels were measured as "B low Average" ( group I), "A verage" (group II), or "Abo Average" (group III). Summary statistics follow: Sample mean Sample Std. Dev 5.48 3.46 4.43 6.88 Sample Size 38 32 24 32 8 10 6 24

1. Recall problem 1 of homework 2: A rehabilitation cen- ter researcher was interested in examining the relationship between physical fitness prior to surgery and the time (in days) for successful completion of physical therapy. The fitness levels were measured as "Below Average" (group I), "Average" (group II), or "Above Average" (group III). Diagnostic plots are found on the back page. (a) From the plots, does it appear that the errors are nor- (b) From the plots, does it appear as if there are outliers? (c) From the plots, does it appear that the groups have mally distributed? Justify your answer. Justify your answer. equal variance? Justify your answer d) Considering the sample size of each group, would you suggest removing any observations? Why or why not. 2. Continue with Problem 1. (a) The Shapiro-Wilks p-value is: 0.8587. State your con- clusion about the appropriate hypothesis in terms of

## Solutions

##### Expert Solution

**Answer:**

(a) from the plots, does it appear that the errors are normally

distributed? Justify your answer.

a) As given in the plots for the problem,

One of the plot that is Q-Q plot to check the normality of the

residuals shows that the errors are normally distributed similarly

histogram shows the same that the errors are normally

distributed.

(b) from the plots,does it appear as if there are outliers?

Justify your answer.

b) As per the given plots,

it doesn't seems to be that any outlier contains in the data of

the researcher which would affect our study.

(c) from the plots, does it appear that the group, have equal

variance? Justify your answer.

c) Take a look at the

As it shows that there are three predicted values and for each

predicted value the residuals are associated with it and to know

that the residuals that are associated are constant this plot shows

the very same thing that the variance among the residuals are

constant.

(d) Considering the sample size of each group, would you suggest

removing any observations? Why or why not.

d) No, i wouldn't remove any observation from the given sample

size because it gives the required result and removing the

observation may occurs the fluctuation or variation amongst the

residuals which would affect our entire study.