You are the manager of a restaurant that delivers pizza to customers. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. From past experience, you can assume that the population standard deviation is 6 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.29
You are the manager of a restaurant that delivers pizza to customers. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. From past experience, you can assume that the population standard deviation is 6 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.29
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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You are the manager of a restaurant that delivers pizza to customers. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current
25
minutes. From past experience, you can assume that the population standard deviation is
6
minutes. A sample of
36
orders using the new delivery process yields a sample mean of
22.29
minutes. Complete parts (a) to (d) below.Question content area bottom
Part 1
a. Using the critical value approach, at the
mean value of
0.05
level of significance, is there evidence that the mean delivery time has been reduced below the previous population 25
minutes?Let
μ
be the population mean. State the null hypothesis,
H0,
and the alternative hypothesis,
H1.
H0:
μ≤25
H1:
μ>25
H0:
μ≥25
H1:
μ<25
H0:
μ≠25
H1:
μ=25
H0:
μ=25
H1:
μ≠25
Part 2
The level of significance is
normal distribution for a sampling distribution. Determine the critical value(s) that divide(s) the rejection and non-rejection region(s).
0.05
and the sample size is
36.
Use the Z-test statistic, and use the The critical value(s) is(are)
enter your response here.
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
Part 3
Calculate the value of the test statistic.
Z=enter your response here
(Round to two decimal places as needed.)Part 4
Make the statistical decision and state the managerial conclusion. Choose the correct answer below.
Do not reject
H0.
There is
sufficient
evidence that the mean time is different from
25
minutes.Reject
H0.
There is
insufficient
evidence that the mean time is different from
25
minutes.Do not reject
H0.
There is
insufficient
evidence that the mean time is different from
25
minutes.Reject
H0.
There is
sufficient
evidence that the mean time is less than
25
minutes.Part 5
b. At the
0.05
level of significance, use the p-value approach.The p-value is
enter your response here.
(Round to three decimal places as needed.)
Part 6
Make the statistical decision and state the managerial conclusion. Choose the correct answer below.
Reject
H0.
There is
insufficient
evidence that the mean time is different from
25
minutes.Reject
H0.
There is
sufficient
evidence that the mean time is less than
25
minutes.Do not reject
H0.
There is
insufficient
evidence that the mean time is different from
25
minutes.Do not reject
H0.
There is
sufficient
evidence that the mean time is different from
25
minutes.Part 7
c. Interpret the meaning of the p-value in (b).
For this test, the p-value is the probability of getting a test statistic greater than the sample result, given that the null hypothesis,
H0,
is true.For this test, the p-value is the probability of getting a test statistic less than the sample result, given that the null hypothesis,
H0,
is true.For this test, the p-value is the probability of getting a test statistic less extreme than the sample result, given that the alternative hypothesis,
H1,
is true.For this test, the p-value is the probability of getting a test statistic more extreme than the sample result, given that the alternative hypothesis,
H1,
is true.Part 8
d. Compare the conclusions in (a) and (b). Are the results the same?
No
Yes
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