Use the data below on response time for two different treatments to answer the following questions. 

	x1	x2	r1	r2
	3	7	_	_
	6	11	_	_
	8	19	_	_
	10	27	_	_

r1 and r2 have values of '_' above as placeholders for the ranks of the observations in sample 1 and 2, respectively. You'll fill in the values for r1 and r2 in part (c). You can cut and paste the data into R, and rearrange it into a data.frame if desired, using the code below.

	x1 = c(3,6,8,10)
	x2 = c(7,11,19,27)

	response = c(x1,x2)
	group = c(rep("group1",4),rep("group2",4))
	dat = data.frame(group,response)
	dat

(a) Test homogeneity of variance (HOV) using the Fmax test. Give the test statistic, the rejection region for the test, and your conclusion.

(b) Use var.test() to test for equal variances. Report the p-value for the test. Is your conclusion the same as for the Fmax test? 

(c) Find the ranks of the observations in the combined dataset and identify them as the values for r1 and r2. Compute (by hand) the Wilcoxon-Mann-Whitney Rank Sum test statistic (S = sum of the ranks in sample 1) for the data.

(d) Test (by hand*) to see if the median for population 2 is significantly greater than that of population 1 using the normal approximation to the sampling distribution for S. Report mu.S, sigma.S, z.s, your p-value, and conclusion at the .05 level. 
     [ z.s = (S - mu.S)/sigma.S ]. 
*you can use R to check your results, but I want to see your hand calculations since you will not have R for exams/quizzes.

(e) Compute the W-M-W Rank Sum test in R using the original 'x' response data (and correct=FALSE, exact=FALSE). Compare to your  results in part (d) and reconcile any differences for the test statistic and p-value (remember that we are using 'S' and R uses 'W', I do not know Y. Do U?).