A national grocer’s magazine reports the typical shopper spends 10 minutes in li

Question

A national grocer’s magazine reports the typical shopper spends 10 minutes in line waiting to check out. A sample of 23 shoppers at the local Farmer Jack’s showed a mean of 9.4 minutes with a standard deviation of 2.2 minutes. Is the waiting time at the local Farmer Jack’s less than that reported in the national magazine? Use the 0.050 significance level.

a. What is the decision rule?

Reject H0: µ 10 and fail to reject H1: µ < 10 when the test statistic is less than_______. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

b. The value of the test statistic is_________ . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   10  
Ha:    u   <   10  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              

df = n - 1 =    22          

tcrit =    -1.717144374   [ANSWER]  

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B)

Getting the test statistic, as              
              
X = sample mean =    9.4          
uo = hypothesized mean =    10          
n = sample size =    23          
s = standard deviation =    2.2          
              
Thus, t = (X - uo) * sqrt(n) / s =    -1.307954052 [ANSWER, TEST STATISTIC]

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