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.

Explanation / Answer

here null hypothesis: all 4 brands are equally probable

alternate hypothesis: brand does not have equal possiblities

b)we will apply chi test on above data

here test stat chi square =12

c) from above degree of freedom =5-1=4.

for 4 degree of freedom ; p value for above test stat =0.0174

d)as p value is less then 0.05 level of significance; we reject manager’s claim that the five types of teddy bears are equally popular

observed Expected Chi square Brand P O E=total*p =(O-E)^2/E 1 0.2 230 200 4.50 2 0.2 170 200 4.50 3 0.2 210 200 0.50 4 0.2 180 200 2.00 5 0.2 210 200 0.50 1000 1000 12.00

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