The UMUC MiniMart sells five different types of coffee mugs

The UMUC MiniMart 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.

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.

Solution

answer of part (a)

Null hypothesis Ho: all five types are equally popular

Alternative hypothesis Ha : at least two are not equally popular

answer of (b)

here we go for chi-square test for goodness of fit

chi-square =sum of ((o-e)²/e)=10 with 4 df

answer of part(c)

in MS-excel we can get p-value of chi-squre=10 with 4 df as (=chidist(10,4))

p-value=.0404 (for chi-squre with value 10 at 4 df)

answer of part (d)

as p-value is less than alpha=0.05 so we reject null hypothesis that there is not sufficient evidence to support the managers\' claim that the five types are equally popular.