A national grocers magazine reports the typical shopper spen

A national grocer’s magazine reports the typical shopper spends 7 minutes in line waiting to check out. A sample of 20 shoppers at the local Farmer Jack’s showed a mean of 6.0 minutes with a standard deviation of 2.0 minutes.

Is the waiting time at the local Farmer Jack’s less than that reported in the national magazine? Use the 0.100 significance level.

a) What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

Reject H₀: µ 7 and fail to reject H₁: µ < 7 when the test statistic is _______

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

Reject H₀

_Or

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   7  
Ha:    u   <   7  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    19          
tcrit =    -   1.327728209      

Thus, Reject Ho when t < -1.328 [ANSWER]

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b)

              
Getting the test statistic, as              
              
X = sample mean =    6          
uo = hypothesized mean =    7          
n = sample size =    20          
s = standard deviation =    2          
              
Thus, t = (X - uo) * sqrt(n) / s =    -2.236067977 = -2.24 [ANSWER]

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c)

As t < -1.328, we REJECT HO.   [ANSWER]