The UMUC MiniMart sells five different types of teddy bears. The manager reports

Question

The UMUC MiniMart sells five different types of teddy bears. The manager reports that the five types are equally popular. Suppose that a sample of 500 purchases yields observed counts for types 1, 2, 3, 4, and 5 shown as the table below. 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.: writing the correct test statistic, without supporting work, will receive no credit. (c)Determine the P-value. 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 five types are equally popular? Justify your answer.

Explanation / Answer

a) null hypothesis: all four types are equally popular.

alternate hypothesis: all four types are not equally popular.

b)

from above test stat X2 =5.5

c) for above degree of freedom =number of categories -1 =5-1 =4

therefore for 4 degree of freedom and above test stat ; p value =0.2397

d) as p value is higher then 0.05 level of significance ; we can not reject null hypothesis.

therefore there is sufficient evidence to support manager's claim that the five types are equally popular.

observed Expected Chi square Type Probability O E=total*p =(O-E)^2/E 1 0.200 120.000 100.00 4.00 2 0.200 95.000 100.00 0.25 3 0.200 90.000 100.00 1.00 4 0.200 95.000 100.00 0.25 5 0.200 100.000 100.00 0.00 1 500 500 5.5000

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