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 1000 purchases yields observed counts 230, 170, 210, 180, and 210 for types 1, 2, 3, 4, and 5, respectively. Use a 0.05 significance level to test the claim that the five types are equally popular. Show all work and justify your answer.

(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. 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 five types of teddy bears are equally popular? Justify your answer.

Type 1 2 3 4 5 Number of Teddy Bears 230 170 210 180 210

Explanation / Answer

a) H0: the five types are equally popular

H1: Atlest one type of teddy bear are not equally popular

b) Given number of Teddy bears are observed frequencies (Oi)

The expected frequencies are calculated by using

Ei = Total number of teddy bears/ No. of types = 1000/5 = 200 for all i = 1,2,3,4,5

Using chisquare test,

Test Statistic, X^2: 12

Critical X^2: 9.48772   Degrees of freedom: 4

c) P-Value: 0.0174

Here P-value < alpha 0.05, we reject H0

d) Thus, there is sufficient evidence to support the manager’s claim that the five types of teddy bears are not equally popular

NO. of Teddy Expected Type Bears (Oi) Freq (Oi-Ei)^2/Ei 1 230 200 4.5 2 170 200 4.5 3 210 200 0.5 4 180 200 2 5 210 200 0.5 Total: 1000 1000 12

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