Irritable bowel syndrome IBS is a nonspecific intestinal dis

Irritable bowel syndrome (IBS) is a nonspecific intestinal disorder characterized by abdominal pain and irregular bowel habits.  Each person in a random sample of 24 patients having periodic attacks of IBS was randomly assigned to one of three treatment groups, A, B, and C.  The number of hours of relief while on therapy is recorded for each patient in the table below.

Treatment

A

B

C

4.7

19.5

22.6

14.8

11.2

16.7

5.1

19.4

12.4

11.9

7.8

16.4

11

11.6

17.2

5.7

9.6

13

15.5

13

14

11.2

13.6

26.1

mean

9.988

13.213

17.300

variance

18.561

18.144

22.871

Give the value of the test statistic used to test H₀: ?_A = ?_B = ?_C.

a.

3.19

b.

2.45

c.

7.51

d.

15.18

e.

5.41

Find the critical value appropriate for comparison with the test statistic in #1 if the .10 significance level is used.

a.

-1.96, 1.96

b.

3.47

c.

2.57

d.

5.78

e.

4.42

Which of the following correctly characterizes the p-value for the test statistic in #1?

a.

p-value < .01

b.

.01 < p-value < .025

c.

.025 < p-value < .05

d.

.05 < p-value < .10

e.

p-value > .10

What is the correct decision (at the .10 significance level) regarding the analysis of variance?

a.

Reject H₀

b.

Do not reject H₀

c.

Reject H_A

d.

Do not reject H_A

e.

Lake Titicaca

		Treatment
	A	B	C
	4.7	19.5	22.6
	14.8	11.2	16.7
	5.1	19.4	12.4
	11.9	7.8	16.4
	11	11.6	17.2
	5.7	9.6	13
	15.5	13	14
	11.2	13.6	26.1
mean	9.988	13.213	17.300
variance	18.561	18.144	22.871

Solution

Give the value of the test statistic used to test H₀: ?_A = ?_B = ?_C.

Answer: e. 5.41

-----------------------------------------------------------------------------------------------------------

Find the critical value appropriate for comparison with the test statistic in #1 if the .10 significance level is used.

Given a=0.1, the critical value is F(0.9, df1=2, df2=21) =2.57 (from F table)

Answer: C.2.57

-----------------------------------------------------------------------------------------------------------

Which of the following correctly characterizes the p-value for the test statistic in #1?

Answer: b. .01 < p-value < .025

-----------------------------------------------------------------------------------------------------------

What is the correct decision (at the .10 significance level) regarding the analysis of variance?

Answer: b. Do not reject H₀

-----------------------------------------------------------------------------------------------------------

ANOVA table
Source	SS	df	MS	F	p-value
Treatment	214.883	2	107.4413	5.41	.0127
Error	417.038	21	19.8589
Total	631.920	23