Answered: has two ways to travel from her home in…

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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Question

Rita has two ways to travel from her home in Norco to her office in Los Angeles. One is to go via the 10 Freeway, and the other is to go via 60 Freeway. In order to determine which way she should travel on a daily basis, Rita has recorded the travel times for samples of twelve trips via the 10 Freeway and twelve trips via the 60 Freeway. The following table gives the travel times (in minutes) for the twenty-four trips.

	Travel times in minutes
10 Freeway	66, 70, 73, 71, 72, 71, 65, 74, 69, 71, 75, 71
60 Freeway	77, 72, 71, 68, 74, 80, 70, 78, 76, 71, 68, 67

Assume that the two populations of travel times are normally distributed and that the population variances are equal. Can we conclude, at the 0.01 level of significance, that the mean travel time via the 10 freeway, μ1, is different from μ2, the mean travel time via the 60 freeway? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table.

a. State the null hypothesis H0 and the alternative hypothesis H1.

b. Find the value of the test statistic. (Round to three or more decimal places.)

c. Find the two critical values at the 0.01 level of significance. (Round to three or more decimal places.)

d. Can we conclude that the mean travel time via the 10 freeway, μ1, is different from μ2, the mean travel time via the 60 freeway?

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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