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

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 13CYU

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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?

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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