Explanation Given info: The table shows the fuel economy for city driving for three different types of automobiles. The level of significance is 0.05. Calculation: The hypotheses are given below: Consider, X ¯ 1 , X ¯ 2 and X ¯ 3 represents the means of small, sedans and luxury, s 1 2 , s 2 2 and s 3 2 represents the variances of samples of small, sedans and luxury. Step-by-step procedure to obtain the test mean and standard deviation using the MINITAB software: Choose Stat > Basic Statistics > Display Descriptive Statistics . In Variables enter the columns Small, Sedans and Luxury . Choose option statistics , and select Mean, Variance and N total . Click OK . Output using the MINITAB software is given below: The sample sizes n 1 , n 2 and n 3 are 4, 5 and 2. The means are X ¯ 1 , X ¯ 2 and X ¯ 3 are 37.25, 35.40 and 26.00. The sample variances are s 1 2 , s 2 2 and s 3 2 are 20.92, 37.30 and 7.00. Boneferroni test: Critical value: Here, k is 3 and degrees of freedom v = N − k Substitute 12 for N and 3 for k in v Degrees of freedom = N − k = 12 − 3 = 9 The critical t -value is obtained using the Table F : The t distribution with the level of significance α = 0.05 . Procedure: Locate 9 in the column of d.f. of the Table F. Obtain the value in the corresponding two tails, 0.05 row. That is, the critical value is 2.262. The formula for finding s W 2 is, s W 2 = ∑ ( n i − 1 ) s i 2 ∑ ( n i − 1 ) That is, s W 2 = ( 4 − 1 ) 20.92 + ( 5 − 1 ) 37.30 + ( 3 − 1 ) 7.00 ( 4 − 1 ) + ( 5 − 1 ) + ( 3 − 1 ) = 62

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Chapter 12.2, Problem 14E

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To compare: The means X¯2 and X¯3 using Bonferroni test.

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Chapter 12.2, Problem 13E

Chapter 12.3, Problem 1AC

Chapter 12 Solutions

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Urban Travel Times Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, sent by residents driving to work. City Population N Driving time T Los Angeles 6489 16.8 Pittsburgh 1804 12.6 Washington 1808 14.3 Hutchinson 38 6.1 Nashville 347 10.8 Tallahassee 48 7.3 An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. a Construct a power model of driving time in minutes as a function of population measured in thousands b Is average driving time in Pittsburgh more or less than would be expected from its population? c If you wish to move to a smaller city to reduce your average driving time to work by 25, how much smaller should the city be?

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To compare: The means X ¯ 2 and X ¯ 3 using Bonferroni test.

Solution Summary: The author explains that the table shows the fuel economy for city driving for three different types of automobiles. The level of significance is 0.05.

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To compare: The means X¯2 and X¯3 using Bonferroni test.

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Chapter 12 Solutions