Question

2. A new chemotherapy drug is released to treat leukemia and researchers suspect that the drug may have fewer side effects than the most commonly used drug to treat leukemia. The two drugs have equivalent efficacy. In order to determine if a larger study should be conducted to look into the prevalence of side effects for the two drugs, set up a Mann-Whitney U test at the alpha equals .05 level and interpret its results.

                        Number of Reported Side-Effects

Old Drug           0          1          3          3          5

New Drug          0          0          1          2          4

Old Drug	New Drug	Total Sample (Ordered Smallest to Largest)		Ranks
		Old Drug	New Drug	Old Drug	New Drug
				R1=	R2=

A) We fail to reject H₀, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 16.5 is greater than the critical U value of 2.

B) We fail to reject H₀, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 8.5 is greater than the critical U value of 2.

C) We reject H₀ in favor of H₁, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 16.5 is greater than the critical U value of 2.

D) We reject H₀ in favor of H₁, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 8.5 is greater than the critical U value of 2.

Answer 1

Answer: B) We fail to reject H₀, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 8.5 is greater than the critical U value of 2.

Explanation: The Mann-Whitney test is performed in the following steps in excel.

Step 1: Sort the combined value of both sample from smallest to largest,

Step 2: The rank for each data point is obtained using the excel function =RANK.AVG(). The screenshot is shown below,

Step 3: Now, place the rank for each data point in the table.

		Ordered		Rank
Old Drug	New Drug	Old Drug	New Drug	Old Drug	New Drug
0	0	0	0	2	2
1	0	1	0	4.5	2
3	1	3	1	7.5	4.5
3	2	3	2	7.5	6
5	4	5	4	10	9
			Sum	31.5	23.5

Step 4: The sum of ranks for both old and new drug is,

Step 5: The U value is obtained using the formula,

Step 5: The critical value for U is obtained from the critical value table for n1 = 4 and n2 = 5 and significance level = 0.05,

Conclusion: Since the U value is greater than the critical value, at a 5% significance level, the null hypothesis is not rejected. Hence we can conclude that both the sample are from same population.