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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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