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
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
minutes. Complete parts (a) to (d) below.
Question content area bottom
Part 1
a. Using the critical value approach, at the
0.05
level of significance, is there evidence that the mean delivery time has been reduced below the previous population mean value of
25
minutes?
Let
μ
be the population mean. State the null hypothesis,
H0,
and the alternative hypothesis,
H1.
A.
H0:
μ≤25
H1:
μ>25
B.
H0:
μ≥25
H1:
μ<25
C.
H0:
μ≠25
H1:
μ=25
D.
H0:
μ=25
H1:
μ≠25
Part 2
The level of significance is
0.05
and the sample size is
36.
Use the Z-test statistic, and use the normal distribution for a sampling distribution. Determine the critical value(s) that divide(s) the rejection and non-rejection region(s).
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.
A.
Do not reject
H0.
There is
sufficient
evidence that the mean time is different from
25
minutes.
B.
Reject
H0.
There is
insufficient
evidence that the mean time is different from
25
minutes.
C.
Do not reject
H0.
There is
insufficient
evidence that the mean time is different from
25
minutes.
D.
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.
A.
Reject
H0.
There is
insufficient
evidence that the mean time is different from
25
minutes.
B.
Reject
H0.
There is
sufficient
evidence that the mean time is less than
25
minutes.
C.
Do not reject
H0.
There is
insufficient
evidence that the mean time is different from
25
minutes.
D.
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).
A.
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.
B.
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.
C.
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.
D.
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
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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