The scale from 0 to 10 (where 0 strongly dislikes and 10 is strongly like) can be represented as below;
Ratings |
|
0 |
Strongly dislike |
1 |
relatively strongly dislike |
2 |
dislike |
3 |
dislike moderately |
4 |
dislike slightly |
5 |
Fair |
6 |
Like slightly |
7 |
like moderately |
8 |
Like |
9 |
relatively strongly like |
10 |
strongly like |
Delegate your assignment to our experts and they will do the rest.
Assuming that Marjin -O Heara should only recommend the production of new jerseys if the color is at least liked by the fans. We have to test whether the information obtained from the sample suggest that the fans like the selected color. We therefore test the null hypothesis that the mean rating is equal to 8.
Null hypothesis: M ean rating of fans = 8, ( H 0: μ=8)
Alternative hypothesis: M ean rating of fans = 8 (
Sample mean,
=6.5, sample standard deviation, s = 0.04, sample size, n= 400, assumed population mean that means the color strongly liked,
= 8
We use z-test since the sample is
We calculate z-statistic using the formula
Z-statistic, Z =
Z = = -750
Z statistic = -750
Assuming 0.05 level of significance we read from z-tables
Lowe tail = 1.645
Decision rule
Reject null hypothesis if Z 1.645
Conclusion
Since -750 < 1.645, we reject the null hypothesis and conclude that there exists insufficient statistical evidence to conclude that the population mean rating by fans is 8. This means that Marjin -O Heara should NOT recommend the production of new jerseys because the color is not liked by the fans.