Question

In an effort to promote a new product, a marketing firm asks participants to rate the effectiveness of ads that varied by length (short, long) and by type of technology (static, dynamic, interactive). Higher ratings indicated greater effectiveness.

Source of Variation	SS	df	MS	F
Length	10
Technology
Length × Technology	154
Error	570	114
Total	864

(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Assume experimentwise alpha equal to 0.05.)

Source of Variation	SS	df	MS	F
Length	10
Technology
Length × Technology	154
Error	570	114
Total	864

State the decision for the main effect of length.

Retain the null hypothesis.Reject the null hypothesis.    

State the decision for the main effect of technology.

Retain the null hypothesis.Reject the null hypothesis.    

State the decision for the interaction effect.

Retain the null hypothesis.Reject the null hypothesis.    

(b) Based on the results you obtained, what is the next step?

Compute pairwise comparisons for the length factor.No further analysis is needed, because none of the effects are significant.    Compute simple main effect tests for the significant interaction.Compute pairwise comparisons for the technology factor.

You may need to use the appropriate table in Appendix C to answer this question.

https://www.webassign.net/priviterastats3/priviterastats3_appendix_c.pdf

Answer 1

a) Level of Factor A, a = 2

Level of Factor B, b = 3

Number of repetition, r = 20

df(A) = a-1 = 1

df(B) = b-1 = 2

df(AB) = (a-1)*(b-1) = 2

df(total) = 114+1+2+2 = 119

SSB = SST -SSA - SSAB- SSE = 130

MSA = SSA/df(A) = 10

MSB = SSB/df(B) = 65

MSAB = SSAB/df(AB) = 77

MSE = SSE/df(error) = 5

F for factor A :

F = MSA/MSE = 2

p-value = F.DIST.RT(2, 1, 114) = 0.1600

F for factor B :

F = MSB/MSE = 13

p-value = F.DIST.RT(13, 2, 114) = 0.0000

F For Interaction :

F = MSAB/MSE = 15.4

p-value = F.DIST.RT(15.4, 2, 114) = 0.0000

ANOVA
Source of Variation	SS	df	MS	F	P-value
Factor A	10	1	10	2	0.1600
Factor B	130	2	65	13	0.0000
Interaction	154	2	77	15.4	0.0000
Error	570	114	5
Total	864	119

State the decision for the main effect of length.

Retain the null hypothesis.

State the decision for the main effect of technology.

Reject the null hypothesis.

State the decision for the interaction effect.

Reject the null hypothesis.

b)

Compute pairwise comparisons for the technology factor.