23 The UMUC MiniMart sells five different types of coffee mu

23. 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 110, 100, 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

Ho: that the five types are equally popular. H1:that the five types are not equally popular.

Given n=500, so it is large sample, so we use chi-square test and it is defined as, chi-square= [(Oi-Ei)²/Ei]=6.

The table value of chi-square with 5-1=4 degrees of freedom at 0.05 is 9.488.

Here chi-square calculated value<chi-square tabulated value. So, we accept null hypothesis. Therefore, that the five types are equally popular.

(d):Yes there is sufficient evidence to support the manager’s claim that the four types are equally popular, because if we combine any of two types, then the table value of chi-square with 4-1=3 degrees of freedom at 0.05 is 7.815. Here chi-square calculated value<chi-square tabulated value. So, we accept null hypothesis,i.e., that the four types are equally popular.