The MiniMart sells four different types of Halloween candy bags. The manager rep

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.  

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