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home / study / math / statistics and probability / statistics and probability questions and answers / with all the fad diets advertised on tv, a researcher wanted to know if there was a significant ... Question: With all the fad diets advertised on TV, a researcher wanted to know if there was a significant d... Edit question With all the fad diets advertised on TV, a researcher wanted to know if there was a significant difference in weight loss depending on which new fad diet you were on. Over the course of 2 weeks, a total of 12 male volunteers who weighed the same and had similar lifestyles were broken up into 3 groups: Diet 1, Diet 2, and Diet 3. Conduct an ANOVA on the following table with alpha = 0.5 to determine if at least one of the diets has significantly different weight loss compared to the other two. Diet 1 -1 5 3 4 Diet 2-13 12 8 3 Diet 3-6 2 1 2 1. SS df MS F Between Within 85.5 Total 182 9. What is the conclusion based on your test statistic? a. Fail to reject the null hypothesis because the test statistic did not fall in the rejection region. There is not sufficient evidence that there is a significant difference in the mean weight loss for at least one of the diets. b. Fail to reject the null hypothesis because the test statistic did fall in the rejection region. There is not sufficient evidence that there is a significant difference in the mean weight loss for at least one of the diets. c. Reject the null hypothesis because the test statistic did not fall in the rejection region. There is sufficient evidence that there is a significant difference in the mean weight loss for at least one of the diets. d. Reject the null hypothesis because the test statistic did fall in the rejection region. There is sufficient evidence that there is a significant difference in the mean weight loss for at least one of the diets.

Answer 1

Ans:

Source	SS	df	MS	F
Between groups	96.5	2	48.25	5.08
within groups	85.5	9	9.5
Total	182	11

p-value=Fdist(5.08,2,9)=0.0334

critical F value=FINV(0.05,2,9)=4.26

As,p-value<0.05,we reject the null hypothesis.

Option d is correct.

Reject the null hypothesis because the test statistic did fall in the rejection region. There is sufficient evidence that there is a significant difference in the mean weight loss for at least one of the diets.