Question

Please answer the 3 part question below. Thank you!

Question 1

Recorded weight losses in lbs for 21 participants of three different diet programs were:

Diet Program #1 #2 #3 Weight Losses in lbs. TS 16 29 18 24 24 19 23 21.86 4.45 21 25 4738 25 29 30 30.71 | 8.96 12 21 24 25 | 18 | 19 | 25 20.57 4.72

a) Run Hartley’s F-max test. Does evidence suggest the variances could be different at
the α = 5% level of significance? Explain, and show any work you can.

b) The other ANOVA conditions (normality, independent random samples) were reasonably
satisfied, so I ran an analysis of variance, and here is the incomplete table of output.
Please fill in the missing values.

c) What is the p-value for this ANOVA test? Based on your p-value, is there significant
evidence at the α = 5% level of significance to suggest the actual mean weight losses
differ? Explain.

Answer 1

a) NULL HYPOTHESIS H0:

0-1 = 0 2 = 0'3

ALTERNATIVE HYPOTHESIS Ha:

0²1 +02+03

alpha=0.05

Fmax = Larger Variance Smaller Variance

F= (8.96)^2/(4.45)^2
F= 4.054

k= 3

d.f= 7-1=6

F critical= 8.38

The calculated value from is smaller than the table value, the variance is homogeneous.

b)

SS	D.F	MS	F stat
SSB=427	2	213.5	5.235
SSW=734	18	40.78
TSS=1161	20

c) The p-value is .016142. The result is significant because p < .05.

Decision: REJECT NULL HYPOTHESIS H0.

Conclusion: We have sufficient evidence to conclude that there is difference in means.