A researcher for a shoe company believes a competitor is cut

A researcher for a shoe company believes a competitor is cutting the cost of his shoes. In the past the competitor\'s average sale price for shoes was $80. The researcher collects 36 pairs of shoes and finds the average cost to be $75. He knows from past research that the standard deviation of the competitor\'s shoe price is $19.20. Is the researcher correct that the shoes are dropping in price? a) state Ho and H1 b) find the critical value c) calculate test value d) calculate P-value for the test statistic e) provide your decision

Solution

Here, we assume alpha = 0.05, as it is not given.

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   80  
Ha:    u   <   80   [ANSWER]

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b)
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    -   1.644853627   [ANSWER]

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c)  
              
Getting the test statistic, as              
              
X = sample mean =    75          
uo = hypothesized mean =    80          
n = sample size =    36          
s = standard deviation =    19.2          
              
Thus, z = (X - uo) * sqrt(n) / s =    -1.5625   [ANSWER]

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d)      
              
Also, the p value is              
              
p =    0.059085123   [ANSWER]

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e)      
              
As P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.          
Thus, there is no significant evidence that the competitor\'s shoe price is dropping. [CONCLUSION]