Question

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.

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

  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 H₀?

• Reject H₀

• Do not reject H₀

Answer 1

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.