Homework SourseAn advertising agency wants to know if the magazine they adv
An advertising agency wants to know if the magazine they advertise in makes a difference in the response to the magazine readers. Each reader was asked to give the advertisement a rank between 0 and 10 (0 for no interest to 10 with high interest). They then survey 10 people that read one of the three different magazines that the company was interested in advertising in. The response of those ten people are:
Magazines
Sports Illistrated
Home and Gardens
In Magazine
5
5
8
4
7
8
7
3
5
8
At a significance level of .05 can we conclude that the mean rank for the advertisement is the same for all three of the magazines?
What is the null hypothesis?
What is your alternative hypothesis?
What is the value of the SST?
What is the SSE?
What is the SSTotal?
What is the degrees of freedom for the treatments?
What is the degrees of freedom for the error?
What is the MST?
What is the MSE?
What is the calculated F distribution?
What is the critical value of the F statistic?
What is your decision?
Fail to reject the null hypothesis
Reject the null hypothesis
Fail to reject the alternative hypothesis
Reject the alternative hypothesis
Interpret the results:
| Magazines | ||
| Sports Illistrated | Home and Gardens | In Magazine |
| 5 | 5 | 8 |
| 4 | 7 | 8 |
| 7 | 3 | 5 |
| 8 |
Solution
An advertising agency wants to know if the magazine they advertise in makes a difference in the response to the magazine readers. Each reader was asked to give the advertisement a rank between 0 and 10 (0 for no interest to 10 with high interest). They then survey 10 people that read one of the three different magazines that the company was interested in advertising in. The response of those ten people are:
One factor ANOVA
Mean
n
Std. Dev
6.0
4
1.83
Sports Illistrated
5.0
3
2.00
Home and Gardens
7.0
3
1.73
In Magazine
6.0
10
1.83
Total
ANOVA table
Source
SS
df
MS
F
Treatment
6.00
2
3.000
0.88
Error
24.00
7
3.429
Total
30.00
9
At a significance level of .05 can we conclude that the mean rank for the advertisement is the same for all three of the magazines?
What is the null hypothesis?
x with bar on top subscript s equals x with bar on top subscript h equals x with bar on top subscript i
x with bar on top subscript s not equal to x with bar on top subscript h not equal to x with bar on top subscript i
x with bar on top subscript s greater or equal than x with bar on top subscript h greater or equal than x with bar on top subscript i
x with bar on top subscript s less or equal than x with bar on top subscript h less or equal than x with bar on top subscript i
What is your alternative hypothesis?
x with bar on top subscript s equals x with bar on top subscript h equals x with bar on top subscript i
x with bar on top subscript s not equal to x with bar on top subscript h not equal to x with bar on top subscript i
x with bar on top subscript s less than x with bar on top subscript h less than x with bar on top subscript i
x with bar on top subscript s greater than x with bar on top subscript h greater than x with bar on top subscript i
What is the value of the SST? 6
What is the SSE? 24
What is the SSTotal? 30
What is the degrees of freedom for the treatments? 2
What is the degrees of freedom for the error? 7
What is the MST? 3
What is the MSE? 3.429
What is the calculated F distribution? 0.88
What is the critical value of the F statistic? 4.74
What is your decision?
Fail to reject the null hypothesis
Reject the null hypothesis
Fail to reject the alternative hypothesis
Reject the alternative hypothesis
Interpret the results:
At a significance level of .05, we can conclude that the mean rank for the advertisement is the same for all three of the magazines.
| One factor ANOVA | |||||
| Mean | n | Std. Dev | |||
| 6.0 | 4 | 1.83 | Sports Illistrated | ||
| 5.0 | 3 | 2.00 | Home and Gardens | ||
| 7.0 | 3 | 1.73 | In Magazine | ||
| 6.0 | 10 | 1.83 | Total | ||
| ANOVA table | |||||
| Source | SS | df | MS | F | |
| Treatment | 6.00 | 2 | 3.000 | 0.88 | |
| Error | 24.00 | 7 | 3.429 | ||
| Total | 30.00 | 9 |
