The UNLV Mini Mart sells five different types of coffee mugs. The manager reports that the five types are equally popular. Suppose that a sample of 500 purchases yields observed counts 120, 90, 110, 100, and 80 for types 1, 2, 3, 4, and 5, respectively.
|
Type
|
1
|
2
|
3
|
4
|
5
|
|
Number of mugs
|
120
|
90
|
110
|
100
|
80
|
Assume we want to use a 0.05 significance level to test the claim that the five types are equally popular.
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the P-value for the test. Show all work; writing the correct P-value, without supporting work, will receive no credit.
(d) Is there sufficient evidence to support the manager's claim that the four types are equally popular? Justify your answer.