Question

# In an effort to promote a new product, a marketing firm asks participants to rate the...

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 142
Error 570 114
Total 802

(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
142
Error 570 114
Total 802

 SOURCE OF VARIATION S.S D.F M.S F CAL P value LENGTH 10 =2-1=1 10/1=10 10/5=2 0.160025 TECHNOLOGY 80 =3-1=2 80/2=40 40/5=8 0.000561 LENGTHX TECHNOLOGY 142 2*1=2 142/2=71 71/5=14.2 0.00000 ERROR 570 114 570/114=5 TOTAL 802 119

alpha= 0.05

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS HA:

F= M.S(LENGTH)/M.S(ERROR)

= 10/5= 2

P VALUE (F= 2, DF1=1 AND DF2= 114) = 0.160025

P value >0.05 henec not significant at0.05.

CONCLUSION: SINCE P VALUE NOT SIGNIFICANT AT 0.05 LEVEL OF SIGNIFICANCE DO NOT REJECT NULL HYPOTHESIS H0.

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS HA: At least one mean is not equal.

alpha= 0.05

F= M.S(TECHNOLOGY)/M.S(ERROR)

= 40/5= 8

P VALUE (F= 8, DF1=2 AND DF2= 114) =0.000561

P value <0.05 henec significant at0.05.

CONCLUSION: SINCE P VALUE SIGNIFICANT AT 0.05 LEVEL OF SIGNIFICANCE REJECT NULL HYPOTHESIS H0. Therefore at least one mean is different.

NULL HYPOTHESIS H0: There is no interaction between length and technology.

ALTERNATIVE HYPOTHESIS HA: There is interaction between length and technology.

alpha= 0.05

F= M.S(LENGTHXTECHNOLOGY)/M.S(ERROR)

= 71/5= 14.2

P VALUE (F= 14.2, DF1=2 AND DF2= 114) =0.00000

P value <0.05 henec significant at0.05.

CONCLUSION: SINCE P VALUE IS SIGNIFICANT THEREFORE WE REJECT NULL HYPOTHESIS AND COCNLUDE THAT THERE IS AN INTERACTION BETWEEN LENGTH AND TECHNOLOGY.

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