The UMUC MiniMart sells four different types of teddy bears. The manager reports that the four types are equally popular. Suppose that a sample of 500 purchases yields observed counts 150, 120, 110, and 120 for types 1, 2, 3, and 4, respectively.

Type	1	2	3	4
Number	150	120	110	120

Assume we want to use a 0.05 significance level to test the claim that the four 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 critical value. Show all work; writing the correct critical value, without supporting work, will receive no credit.

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