Question

#4

A research paper describes an experiment in which 74 men were assigned at random to one of four treatments.

1. viewed slides of fit, muscular men
2. viewed slides of fit, muscular men accompanied by diet and fitness-related text
3. viewed slides of fit, muscular men accompanied by text not related to diet and fitness
4. did not view any slides

The participants then went to a room to complete a questionnaire. In this room, bowls of pretzels were set out on the tables. A research assistant noted how many pretzels were consumed by each participant while completing the questionnaire. Data consistent with summary quantities given in the paper are given in the accompanying table.

Treatment 1	Treatment 2	Treatment 3	Treatment 4
9	6	1	5
7	8	5	1
4	0	2	5
13	4	0	7
1	9	4	5
2	8	0	1
5	6	4	0
9	2	3	0
12	7	3	3
5	8	5	4
2	8	5	1
0	5	7	4
6	14	8	2
4	9	3	2
10	0	0
7	6	6
0	3	4
11	12
	5
	6
	10
	8
	6
	2
	10

Do these data provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments? Test the relevant hypotheses using a significance level of 0.05.

Calculate the test statistic. (Round your answer to two decimal places.)

F =

Answer 1

H0: μ1 = μ2 = μ3=μ4

H1: There is at least one mean difference among the populations.

Applying ANOVA from excel: (Data-data analysis:ANOVA:single factor:input data array)

Source of Variation	SS	df	MS	F	P-value
Between Groups	171.8525	3	57.2842	5.5452	0.0018
Within Groups	723.1340	70	10.3305
Total	894.9865	73

from above

test statistic F =5.55

since p value <0.05 , we reject Ho and conclude that mean number of pretzels consumed is not the same for all four treatments