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	156
Error	570	114
Total	826

(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	156
Error	570	114
Total	826

Please help, I'm having trouble answering. Thank you!

Answer 1

So, using this information we can now directly obtain the ANOVA table.

Note that in our example, p=2. q=3 and m=20.

and SS(due to technology)= Total SS - (SS due to length+SS due to interaction effect+ SS due to error)

Hence, 2-way ANOVA table:

Sources of Variation	SS	df	MS	F
Length	10	1	10	2
Technology	90	2	45	9
Length*technology	156	2	78	15.6
Error	570	114	5
Total	824	119

For the three hypotheses, Critical values are as follows:

1)

2)

3)

As can be seen, we reject the null hypothesis 2 and 3, since the tabulated values of F > critical values, and conclude that there is significant effect of the factor Technology and the interaction effect on the effectiveness of ads.