Hi can you please answer the questions down below based on the data table and give a detailed explanation?

A rehabilitation center 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). Summary statistics follow: I II III Overall Sample mean 38 32 24 32 Sample Std. Dev 5.48 3.46 4.43 6.88 Sample Size 8 10 6 24Hypothesis Testing (a) Based on the sample values, would you conclude that the variance for each group is constant? Why or why not. (b) What group appears to have the fastest recovery time? Do you believe it is statistically signicantly faster than the group that has the slowest recovery time? Hint: Analyze the variance/ standard deviaiton. (c) State the null and alternative for testing if the population means are all equal. ((1) Find the value of the test-statistic1 and the approximate the pvalue for the test in (c). (e) State your conclusion in terms of the problem if a: = 0.01