Question #2003424: Analysis of Variance


Question: A physician who specializes in weight control has three different diets she recommends. As an experiment, she randomly selected 15 patients and then assigned 5 to each diet. After three weeks, the following weight losses, in pounds, were noted. At the .05 significance level, can she conclude that there is a difference in the mean amount of weight loss among the three diets?

Plan A Plan B Plan C
5 6 7
7 7 8
4 7 9
5 5 8
4 6 9

a. State the null hypothesis and alternative hypothesis.

b. What is the decision rule?

c. Read this carefully. Compute SS total, SSE, and SST. If you calculate manually, use the table that begins on p. 6 (below) to do your calculations. If you use Excel or any other software to calculate your SS total, SSE, and SST, you must embed your Excel spreadsheet/worksheet into this section. In either case, manually or Excel, place your calculations on SS total, SSE, and SST in the ANOVA table below.

d. Complete an ANOVA table. Place your answers in the appropriate box below.

Source of Variation Sum of Squares Degrees of Freedom Mean Squares F

e. What is your decision?

ANOVA Worksheet for Manual Calculation

Treatment 1 Treatment 2 Treatment 3
X X2 X X2 X X2 Total
Tc = \[\sum{{}}\]x=
(\[\sum{{}}\]x)2/n =
nc =
X2 = \[\sum{{}}\] X2=

SS total = \[\sum{X}\] 2 – ( \[\sum{X}\] )2 / n

\[\sum{X}\] 2 is the X values squared and then summed

( \[\sum{X}\] )2 is the X values summed and then squared

n is the total number of observations

Sum of Squares Treatment = SST = \[\sum{{}}\] (T2 c / nc ) – ( \[\sum{X}\] )2 / n

T2 c is the column total for each treatment

nc is the number of observations (sample size) for each treatment

Sum of Squares Error = SSE = SS total – SST

Solution: The solution consists of 519 words (5 pages)
Deliverables: Word Document

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