Question

Here comes BBA (Body-By-Agbegha) program again! A group of women of comparable age, weight and height was subjected to three weight loss treatments - BBA1, BBA2 and BBA3.   The table below shows the weight loss for the women.

BBA1	BBA2	BBA3
21	27	14
11	34	32
19	28	29
21	31	30
26	19	25
26	30	11
11	22	22
13	38	19
12	31	23

Test to see whether there is any significant difference in the mean weight loss between the programs. Use a 5% level of significance.

State the null and alternative hypotheses.

Find the critical F value.

State a decision rule.

Find the value of the F Statistics.

Find the p-value.

State your decision.

Draw an appropriate conclusion using the context of the problem.

Answer 1

using excel data analusis tool for one way anova,we get

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
BBA1	9	160	17.778	38.194
BBA2	9	260	28.889	33.611
BBA3	9	205	22.778	51.444
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	557.4074	2	278.7037	6.7839	0.0046	3.4028
Within Groups	986.0000	24	41.0833
Total	1543.4074	26

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null hypothesis:all means are equal

or

null hypothesis:there is no significant difference in the mean weight loss between the programs

alternate hypothesis:not all means are equal

or

alternate hypotheis:there is a significant difference in the mean weight loss between the programs

critical F value = 3.4028

a decision rule

if F-stat>3.4028,then reject H0,otherwise not

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F Statistics.=6.7839

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p-value=0.0046

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since,p-value<alpha=0.05,null hypothesis is rejected

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conclusion:there is enough evidence that there is a significant difference in the mean weight loss between the programs