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Statistics: Confidence Interval Problem

See the attached Q8 file for proper format.

Only use the attached documents to assist with your solution and a scientific calculator. Please show all working out so I can understand how you have solved the question, and do not use Excel.

Q8
A study was carried out by JT Co. Regarding the stopping distance of a 1300 kilogram car under perfect
weather conditions at various driving speeds. The results are shown in the following table:
Speed of the Car
(in kilometres per hour)
(x)
Stopping Distance (in metres)
(y)
30 11
50 19
60 34
80 52
100 85
110 95

To save calculation time, you can use the following sums and sums of squares and cross-products for
subsequent calculations:

a. Construct a scatter diagram for these data.
b. Calculate the least squares regression line with stopping distance (y) as the dependent variable and
speed of the car (x) as the independent variable.
c. Plot the regression line on your scatter diagram. Show your calculations for x = 40 and x = 100.
d. Interpret the value "b" in the sample regression line.
e. Construct a 99% confidence interval for B. [Note: Assume Sb = 0.0976].
f. Construct a 95% prediction interval for the stopping distance of a car when its speed is 70 kph. Assume
Se = 6.68.
g. What percent of stopping distance is explained by its linear relationship with the speed of the car?

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Solution Summary

This solution provides a detailed, step by step calculation of the given statistics problem.

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