Question

Problem 3

An experiment was conducted to compare the effectiveness of three new analgesics (painkillers), ?1, ?2, ?3. A clinic evaluated a large group of patients and identified 24 patients with a moderate level of pain. Each of the 24 people was then randomly assigned to one of the three new analgesics. The patients were then placed on therapies and the percentage reduction in pain level was assessed for each patients. Apply the Kruskal-Wallace test to determine if there is a difference in the distributions of pain reduction for the three analgesics. ?=.05.

% Reduction	Analgesic
3	A1
1.2	A1
1	A1
0.7	A1
1.1	A1
0.6	A1
1.2	A1
0.1	A1
0.7	A1
1.9	A1
0.6	A1
0	A1
1.6	A1
4	A1
1	A1
1.8	A2
6.3	A2
5.2	A2
3.7	A2
5.4	A2
2.9	A2
6	A2
0.3	A2
3.6	A2
9.3	A2
2.8	A2
0	A2
8.1	A2
19.9	A2
0.3	A2
1.3	A3
12.6	A3
10	A3
10.5	A3
10.8	A3
5.9	A3
12.1	A3
0.6	A3
18.6	A3
18.7	A3
5.5	A3
0	A3
18.2	A3
22.3	A3
0.6	A3

Question 15:

Choose the correct alternate hypothesis for this test.

a. Ha: All of the analgesic's effects differ with respect to pain reduction.

b. Ha: At least one of the three analgesics differs from the others with respect to pain reduction.

c. Ha: All of the analgesic's affects are the same with respect to pain reduction.

d. Ha: All analgesic's distributions differ with respect to pain reduction.

Question 16:

Provide the correct test statistic. Round answer to four decimal places.

Question 17:

Choose the correct p-value for this test.

a. 0.0039

b. 0.0025

c. 0.1666

d. <0.0001

Question 18:

Choose the correct conclusion for this hypothesis test.

a. Reject Ho. There is sufficient sample evidence to conclude that at least one of the three analgesics differs from the others with respect to pain reduction.

b. Fail to reject Ho. There is insufficient sample evidence to conclude that at least one of the three analgesics differs from the others with respect to pain reduction.

c. Fail to reject Ho. There is insufficient sample evidence to conclude that all of the three analgesics are the same with respect to pain reduction.

d. Reject Ho. There is sufficient sample evidence to conclude that all of the three analgesics are the

Answer 1

Using Minitab Statistical software:

Kruskal-Wallis Test: % Reduction versus Analgesic

Kruskal-Wallis Test on % Reduction

Analgesic N Median Ave Rank Z
A1 15 1.000 14.1 -3.20
A2 15 3.700 24.3 0.46
A3 15 10.500 30.6 2.74
Overall 45 23.0

H = 12.00 DF = 2 P = 0.002
H = 12.01 DF = 2 P = 0.002 (adjusted for ties)

Question 15:correct Alternative hypothesis is:

b. Ha: At least one of the three analgesics differs from the others with respect to pain reduction.

Question 16:

Test statistic =12.01

Question 17:

P-value= b) 0.0025

Question 18:

Conclusion:

P-value 0.0025<0.05 so we reject H0

a. Reject Ho. There is sufficient sample evidence to conclude that at least one of the three analgesics differs from the others with respect to pain reduction.