Almost all U.S. light-rail systems use electric cars that run on tracks built at

Question

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.

Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
( , )

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 (to 1 decimal).
( , )

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.

City Miles of Track Ridership (1000s) Cleveland 15 17 Denver 17 37 Portland 38 83 Sacramento 21 33 San Diego 47 77 San Jose 31 32 St. Louis 34 44

Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
( , )

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 (to 1 decimal).
( , )

Explanation / Answer

Excel used.

Regression Analysis

r²

0.713

n

7

r

0.844

k

1

Std. Error

14.413

Dep. Var.

Ridership (1000s)

ANOVA table

Source

SS

df

MS

F

p-value

Regression

2,582.1492

1  

2,582.1492

12.43

.0168

Residual

1,038.7080

5  

207.7416

Total

3,620.8571

6  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=5)

p-value

95% lower

95% upper

Intercept

-4.7629

15.4325

-0.309

.7701

-44.4334

34.9077

Miles of Track

1.7554

0.4979

3.526

.0168

0.4755

3.0353

Predicted values for: Ridership (1000s)

95% Confidence Interval

95% Prediction Interval

Miles of Track

Predicted

lower

upper

lower

upper

Leverage

30

47.898

33.836

61.960

8.269

87.527

0.144

Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
( , )

95% confidence interval for the mean weekday ridership = (33.836, 61.960)( 1000s)

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 (to 1 decimal).

95% prediction interval for the mean weekday ridership = (8.269, 87.527)( 1000s)

Regression Analysis

r²

0.713

n

7

r

0.844

k

1

Std. Error

14.413

Dep. Var.

Ridership (1000s)

ANOVA table

Source

SS

df

MS

F

p-value

Regression

2,582.1492

1  

2,582.1492

12.43

.0168

Residual

1,038.7080

5  

207.7416

Total

3,620.8571

6  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=5)

p-value

95% lower

95% upper

Intercept

-4.7629

15.4325

-0.309

.7701

-44.4334

34.9077

Miles of Track

1.7554

0.4979

3.526

.0168

0.4755

3.0353

Predicted values for: Ridership (1000s)

95% Confidence Interval

95% Prediction Interval

Miles of Track

Predicted

lower

upper

lower

upper

Leverage

30

47.898

33.836

61.960

8.269

87.527

0.144

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