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 110,100,110,100, and 80 for types 1, 2, 3,4,and 5, respectively. TYPE 1 2 3 4 5 NUMBER OF MUGS 110 100 110 100 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

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