1-) A national grocer’s magazine reports the typical shopper spends 9.5 minutes in line waiting to check out. A sample of 27 shoppers at the local Farmer Jack’s showed a mean of 9.1 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 0.010 significance level.
Reject H0: µ ≥ 9.5 and fail to reject H1: µ < 9.5 when the test statistic is (less than/ greater than/ equal to) ___________ , _______________
b. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)
Value of the test statistic ______________
c. What is your decision regarding H_{0}?
Reject H_{0}
Do not reject H_{0}
Solution :
= 9.5
=9.1
S =2.2
n = 27
This is the left tailed test .
The null and alternative hypothesis is ,
H0 : > 9.5
Ha : < 9.5
Test statistic = t
= ( - ) / S / n
= (9.1 -9.5 ) / 2.2 / 27
= −0.945
Test statistic = t = −0.945
P-value = 0.1767
= 0.01
P-value >
0.1767 > 0.01
Fail to reject the null hypothesis .
There is not sufficient evidence to claim that the population mean μ is less than 9.5, at the 0.01 significance level.
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