Question

In: Statistics and Probability

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 5
Technology
Length × Technology 154
Error 570 114
Total 819

(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 5
Technology
Length ×
Technology
154
Error 570 114
Total 819

Solutions

Expert Solution

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS HA:

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

= 5/5= 1

P VALUE (F= 1, DF1=1 AND DF2= 114) = 0.3711

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)

= 45/5= 9

P VALUE (F= 9, DF1=2 AND DF2= 114) =0.00023

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)

= 77/5= 14.2

P VALUE (F= 15.4, 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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