The MiniMart sells four different types of Halloween candy b

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. (

Solution

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.