Question

Three students, Linda, Tuan, and Javier, are given five laboratory rats
each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats
Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a
specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a
significance level of 10%, test the hypothesis that the three formulas produce the same mean
weight gain.
Linda Tuan Javier
43.5 47.0 51.2
39.4 40.5 40.9
41.3 38.9 37.9
46.0 46.3 45.0
38.2 44.2 48.6
a. State the null and alternative hypotheses
b. What is the test statistic?
c. Using a .05 significance level, what is the decision rule?
d. Show the test statistic and essential calculations.
e. Interpret you results
f. Conduct a Post Hoc Tukey

Answer 1

applying ANOVA:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Linda	5	208.4	41.68	9.857
Tuan	5	216.9	43.38	12.667
Javier	5	223.6	44.72	29.557
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	23.212	2	11.606	0.668536	0.530548	3.885294
Within Groups	208.324	12	17.36033
Total	231.536	14

a)

the hypothesis will be:

Null hypothesis: All means are equal

Alternate hypothesis: Atleast one group has a different mean

b)

test statistic F =0.66

c)

p-value=0.5305 < 0.05 we do not reject Ho

d)

F-test statistic we will use to compare more than two means.

F= Variation between sample mean/Variation within the sample

= 0.66

e) Interpretation :

We do not reject H0 means there is no evidence against H0 .