Question

A national grocer’s magazine reports the typical shopper spends eight minutes in line waiting to check
out. A sample of 24 shoppers at the local Farmer Jack’s showed a mean of 7.5 minutes with a standard
deviation of 3.2 minutes. Is it reasonable to conclude that the waiting time at the local Farmer Jack’s is
less than that reported in the national magazine? Use the 0.05 significance level.

Use the information above to solve the following questions:

a. What is the null hypothesis statement for this problem?
b. What is the alternative hypothesis statement for this problem?
c. What is alpha for this analysis?
d. What is the most appropriate test statistic for this problem (choose one of the following)
• T
• Z
e. What is the value of the test statistic for the most appropriate analysis?
f. What is the lower bound value of the critical statistic? If one does not exist (i.e. is not applicable
for this type analysis), document N/A as your response.
g. What is the upper bound value of the critical statistic? If one does not exist (i.e. is not applicable
for this type analysis), document N/A as your response.
h. Is it reasonable to conclude that the waiting time at the local Farmer Jack’s is less than that
reported in the national magazine? (choose one of the following)
• Yes
• No
i. What is the p-value for this analysis?

Answer 1

NULL HYPOTHESIS H0: MINUTES

ALTERNATIVE HYPOTHESIS Ha: MINUTES

LEVEL OF SIGNIFICANCE

T is the most appropriates test statistic because population standard deviation is known.

test statistic t= xbar-mu/s/sqrt(n)

t= 7.5-8/3.2/sqrt(24)

t= -0.5/3.2/4.90

t= -0.76563

f) Degrees of freedom= 24-1=23

Critical value of t= -1.71

g) NA

h) Since Critical value SMALLER THAN THE CALCULATED VALUE FOR LEFT TAILED TEST THEREFORE NOT SIGNIFICANT.

DECISION: DO NOT REJECT NULL HYPOTHESIS H0.

NO. It is NOT reasonable to conclude that the waiting time at the local Farmer Jack’s is less than that
reported in the national magazine.

i) The p-value is 0.224568.