Cautions: DO NOT use a regression analysis calculator (Excel, minitab, etc.). You can use acalculator for step-by-step calculations like calculating means, sum of the deviations ofsquares, e.g. but you are not allowed to use a whole regression analysis calculator. A) Develop a 95% confidence interval for the mean weekday ridership for alllight-rail systems with 30 miles of track.B) Suppose that Charlotte is considering construction of a light-rail system with30 miles of track. Develop a 95% prediction interval for the weekdayridership for the Charlotte system. Do you think that the prediction intervalyou developed would be of value to Charlotte planners in anticipating thenumber of weekday riders for their new lightrail system? Explain. 1. Almost all U.S. light-rail systems use electric cars that run on tracks built at streetlevel. The Federal Transit Administration claims light-rail is one of the safest modesof travel, with an accident rate of .99 accidents per million passenger miles ascompared to 2.29 for buses. The following data show the miles of track and theweekday ridership in thousands of passengers for six light-rail systems (USA Today,January 7, 2003).CityMiles of TrackRidership (1000s)Cleveland1715Denver1936Portland4078Sacramento2328San DiegoSan JoseSt. Lois507533313742Develop a 95% confidence interval for the mean weekday ridership for allA)light-rail systems with 30 miles of track.Suppose that Charlotte is considering construction of a light-rail system with30 miles of track. Develop a 95% prediction interval for the weekdayridership for the Charlotte system. Do you think that the prediction intervalyou developed would be of value to Charlotte planners in anticipating thenumber of weekday riders for their new lightrail system? Explain.B)Cautions: DO NOT use a regression analysis calculator (Excel, minitab, etc.). You can use acalculator for step-by-step calculations like calculating means, sum of the deviations ofsquares, e.g. but you are not allowed to use a whole regression analysis calculator.

Simple linear regression model: A simple linear regression model is given as y^ = b0 + bx + e…

Answered: Develop a 95% confidence interval for…

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Author:Amos Gilat

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Cautions: DO NOT use a regression analysis calculator (Excel, minitab, etc.). You can use a
calculator for step-by-step calculations like calculating means, sum of the deviations of
squares, e.g. but you are not allowed to use a whole regression analysis calculator.

A) Develop a 95% confidence interval for the mean weekday ridership for all
light-rail systems with 30 miles of track.

B) Suppose that Charlotte is considering construction of a light-rail system with
30 miles of track. Develop a 95% prediction interval for the weekday
ridership for the Charlotte system. Do you think that the prediction interval
you developed would be of value to Charlotte planners in anticipating the
number of weekday riders for their new lightrail system? Explain.

1. Almost all U.S. light-rail systems use electric cars that run on tracks built at street
level. The Federal Transit Administration claims light-rail is one of the safest modes
of travel, with an accident rate of .99 accidents per million passenger miles as
compared to 2.29 for buses. The following data show the miles of track and the
weekday ridership in thousands of passengers for six light-rail systems (USA Today,
January 7, 2003).
City
Miles of Track
Ridership (1000s)
Cleveland
17
15
Denver
19
36
Portland
40
78
Sacramento
23
28
San Diego
San Jose
St. Lois
50
75
33
31
37
42
Develop a 95% confidence interval for the mean weekday ridership for all
A)
light-rail systems with 30 miles of track.
Suppose that Charlotte is considering construction of a light-rail system with
30 miles of track. Develop a 95% prediction interval for the weekday
ridership for the Charlotte system. Do you think that the prediction interval
you developed would be of value to Charlotte planners in anticipating the
number of weekday riders for their new lightrail system? Explain.
B)
Cautions: DO NOT use a regression analysis calculator (Excel, minitab, etc.). You can use a
calculator for step-by-step calculations like calculating means, sum of the deviations of
squares, e.g. but you are not allowed to use a whole regression analysis calculator.

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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