The UMUC MiniMart sells five different types of coffee mugs. The manager reports

Question

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

(c) Determine the P-value for the test. Show all work

(d) Is there sufficient evidence to support the manager’s claim that the four types are equally popular? Justify your answer

Type 1 2 3 4 5 # of mugs 120 90 110 100 80

Explanation / Answer

a) H0: All are equally popular

   Ha: Atleast two are not equally popular

Two tailed chi square test

DF = 4

Prepare contingency table as follows:

Test statistic = 10

p value = 0.040428. The result is significant at p < 0.05.

Hence reject null hypothesis

There is statistical evidence to prove that all are not equally popular

Type 1 2 3 4 5 # of mugs 120 90 110 100 80 500 Expected 100 100 100 100 100 500 chi square 4 1 1 0 4 10

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