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Name: A manager of a pizza restaurant has changed the restaurant's delivery
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Description: A manager of a pizza restaurant has changed the restaurant's delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. A sample of 36 orders using the new delivery process yields

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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A manager of a pizza restaurant has changed the restaurant's delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.5 minutes and a sample standard deviation of 6 minutes.

Using the critical value approach, at the 0.05 level of significance, is there evidence that the population means the delivery time has been reduced below the previous population means the value of 25 minutes?

State the null and alternative hypotheses for this test.

H0: μ≥25

H1: μ<25

H0: μ<25

H1: μ≥25

H0: μ>25

H1: μ≤25

H0: μ≤25

H1: μ>25

H0: μ≤22.5

H1: μ>22.5

H0: μ≥22.5

h1: μ<22.5

What is the test statistic for this test?

tStat=___

What is the conclusion for this test?

Using the p-value approach, at the 0.05 level of significance, is there evidence that the population means the delivery time has been reduced below the previous population means the value of 25 minutes?

What is the p-value for this test?

p-value=___ (Type an integer or a decimal. Round to three decimal places as needed.)

What is the conclusion for this test?

Since the p-value is __A__ than α, __B__ the null hypothesis and conclude that there is __C__ evidence that the population means delivery time has been reduced below the previous population means value of 25 minutes.

A: less or greater

B: reject or do not reject

C: Sufficient or insufficient

Interpret the meaning of the p-value in this problem. Choose the correct answer below.

A. The p-value is the probability of selecting a sample of deliveries that has a mean delivery time of 25 minutes or more, given that the population means delivery time is 22.5 minutes.

B. The p-value is the probability of selecting a sample of deliveries that has a mean delivery time of 22.5 minutes or less, given that the population means delivery time is 25 minutes.

C. The p-value is the probability of selecting a sample of deliveries that has a mean delivery time of 22.5 minutes or more, given that the population means delivery time is 25 minutes.

D. The p-value is the probability of selecting a sample of deliveries that has a mean delivery time of 25 minutes or less, given that the population means delivery time is 22.5minutes.

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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