The general manager of a large discount chain was considerin

The general manager of a large discount chain was considering location of a new store in a small mid-western city. The decision was dependent upon the per capita retail sales for the city being significantly greater than $4,500. A sample of 500 residents was taken, and showed a mean of $4,780. The population standard deviation is known as $25.
State the null and alternative hypotheses.

Specify the rejection region for the significance value (alpha) as 0.01.

Calculate the sample (test) statistic.

Calculate the p value.

What is your conclusion?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   4500  
Ha:    u   >   4500   [ANSWER]

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As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    +   2.326347874      

Thus, we Reject Ho if z > 2.326. [ANSWER]

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Getting the test statistic, as              
              
X = sample mean =    4780          
uo = hypothesized mean =    4500          
n = sample size =    500          
s = standard deviation =    25          
              
Thus, z = (X - uo) * sqrt(n) / s =    250.4396135   [ANSWER, TEST STATISTIC]

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As this is a very large z value, the p value is              
              
p =    0   [ANSWER]

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As z > 2.326, we reject Ho.

There is significant evidence that the per capita retail sales for the city is significantly greater than $4,500. [CONCLUSION]