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Description: You are the manager of a restaurant for a fast-food franchise. Last month, the mean waiting time at the drive-through window for branches in your geographical region, as measured from the time a customer places an order until the time the custome

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 for a fast-food franchise. Last month, the mean waiting time at the drive-through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.6 minutes. You select a random sample of 81 orders. The sample mean waiting time is 3.38 minutes, with a sample standard deviation of 0.9 minute.

1. At then 0.01 level of significance, is there evidence that the population mean waiting time is different from 3.6 minutes? State the null and alternative hypotheses

H0:

H1:

Determine the test statistic.

The test statistic is ____

the t critical is t.025,63 = 1.9983 since the t tstat is not more than t critical do not reject

State the conclusion.

__A___ H0. There is __B___ evidence to conclude that the population mean waiting time is different from 3.6 minutes.

A: Reject or do not reject

B: sufficient or insufficient

2. Because the sample size is 81, do you need to be concerned about the shape of the population distribution when conducting the t test in (a)? Explain. Choose the correct answer below.

A. Yes, because n is equal to 81, the sampling distribution of the t test cannot be determined. In general, the t test requires a larger sample size.

B. No, because n is equal to 81, the sampling distribution of the t test is approximately normal. In general, the t test is appropriate for a large sample size.

C. Yes, because n is equal to 81, the sampling distribution of the t test cannot be determined. In general, the t test is only appropriate for a normally distributed sample.

D. No, because n is equal to 81, the sampling distribution of the t test is approximately normal. In general, the t test is appropriate for this sample size since n > 30

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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