The MiniMart sells four different types of Halloween candy bags. The manager rep
ID: 3378405 • Letter: T
Question
The MiniMart sells four different types of Halloween candy bags. The manager reports that the four types are equally popular. Suppose that a sample of 500 purchases yields observed counts 150, 110, 130, and 110 for types 1, 2, 3, and 4, respectively. Type 1 2 3 4 Number of Bags 150 110 130 110 Assume we want to use a 0.10 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 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. (
Explanation / Answer
a)
Ho: The probability of choosing the bags are equal for each kind of bag.
Ha: The probability of choosing the bags not are equal for each kind of bag.
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b)
Doing an observed/expected value table,
O E (O - E)^2/E
150 125 5
110 125 1.8
130 125 0.2
110 125 1.8
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 8.8 [ANSWER]
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c)
As df = a - 1,
a = 4
df = a - 1 = 3
Also, the p value is, using table/technology,
p = 0.032071641 [ANSWER]
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D)
As p < 0.10, we REJECT THE NULL HYPOTHESIS.
Thus, there is NO sufficient evidence to support the manager’s claim that the four types are equally popular, as we reject the null hypothesis.