In television’s early years, most commercials were 60 seconds long. Now, however, commercials can be any length. The objective of commercials remains the same – to have as many viewers as possible remember the product in a favorable way and eventually buy it. In an experiment designed to investigate determinants of viewers’ memory of products advertised on commercial television, a random sample of 60 people were asked to watch a 1-hour television program. In the middle of the program, a commercial advertising a particular product appeared. Some viewers watched a commercial that lasted for 20 seconds, others watched one that lasted for 24 seconds, 28 seconds, …, 60 seconds. (You should consider the length of the commercial a quantitative variable). In addition to varying length, the theme of commercial was humorous (H), musical (M), or serious (S). The type and length (Length) of commercial viewed by each individual was randomly determined. After the show, a memory test was given, and a score (Test), measured on a 30-point scale, was recorded for each participant. Obtain the results for the least squares regression of Test score on the commercial Length and the commercial Type. Include the S (serious) and M (musical) categories in the equation.
Perform the Partial F-test for the statistical significance of Type of commercial at the 5% level. State the null and alternative hypotheses, show the calculation of the Partial-F statistic, give the decision rule, and state the conclusion in terms of the business problem.
Data:
Test Length Type
24 52 1
20 40 2
16 36 2
11 28 1
10 44 3
4 16 1
24 48 1
18 52 2
16 60 3
15 44 2
14 36 1
15 44 2
24 60 3
10 24 3
1 32 1
8 40 3
9 24 1
0 32 3
17 52 2
9 36 3
26 60 2
28 56 1
15 20 1
8 40 3
2 48 1
0 20 2
11 24 3
8 36 3
24 60 1
10 44 1