Charmaine has two ways to travel from her home in Norco to her office in Los Angeles. One is to go via the San Bernardino Freeway, and the other is to go via the Pomona Freeway. Recently, a lane was added to the San Bernardino Freeway. So, Charmaine wants to determine if it is now faster to take the San Bernardino Freeway than the Pomona Freeway. She selected a random sample of 11 of her trips via the San Bernardino Freeway and a random sample of 11 of her trips via the Pomona Freeway. The two samples were chosen separately, so that the selection of the trips via the San Bernardino Freeway did not affect the selection of the trips via the Pomona Freeway. Charmaine recorded the travel times (in minutes) for the trips in each of the two samples. The following table gives the data, sample means, and sample standard deviations. Travel times in minutes Sample mean Sample standard deviation S.B. Fwy 79, 63, 73, 63, 61, 67, 75, 60, 73, 60, 79 68.5 7.5 Pomona Fwy 77, 73, 74, 68, 79, 69, 77, 76, 78, 67, 80 74.4 4.6 Send data to calculator Send data to Excel (a)Are the two samples of trips independent or paired (dependent) samples? Choose the best answer. independent samples paired (dependent) samples (b)Charmaine wants to use the data to determine whether the mean travel time via the San Bernardino Freeway is less than the mean travel time via the Pomona Freeway. Assume that both populations are approximately normally distributed and that the population variances are equal. Choose the appropriate test statistic for the hypothesis test that would be performed. Then calculate that statistic. Carry your intermediate computations to three or more decimal places. Round your answer to three decimal places. (If necessary, consult a list of formulas.) =z =t It is unclear which test statistic to use.

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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Charmaine has two ways to travel from her home in Norco to her office in Los Angeles. One is to go via the San Bernardino Freeway, and the other is to go via the Pomona Freeway. Recently, a lane was added to the San Bernardino Freeway. So, Charmaine wants to determine if it is now faster to take the San Bernardino Freeway than the Pomona Freeway. She selected a random sample of 11 of her trips via the San Bernardino Freeway and a random sample of 11

of her trips via the Pomona Freeway. The two samples were chosen separately, so that the selection of the trips via the San Bernardino Freeway did not affect the selection of the trips via the Pomona Freeway. Charmaine recorded the travel times (in minutes) for the trips in each of the two samples. The following table gives the data, sample means, and sample standard deviations.

	Travel times in minutes	Sample mean	Sample standard deviation
S.B. Fwy	79, 63, 73, 63, 61, 67, 75, 60, 73, 60, 79	68.5	7.5
Pomona Fwy	77, 73, 74, 68, 79, 69, 77, 76, 78, 67, 80	74.4	4.6

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(a)Are the two samples of trips independent or paired (dependent) samples? Choose the best answer.

independent samples

paired (dependent) samples

(b)Charmaine wants to use the data to determine whether the mean travel time via the San Bernardino Freeway is less than the mean travel time via the Pomona Freeway. Assume that both populations are approximately normally distributed and that the population variances are equal.

Choose the appropriate test statistic for the hypothesis test that would be performed. Then calculate that statistic. Carry your intermediate computations to three or more decimal places. Round your answer to three decimal places. (If necessary, consult a list of formulas.)

	=z
	=t
	It is unclear which test statistic to use.

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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