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AP Statistics / Mr. Hansen |
Name: _________________________ |
AP
Free-Response Practice II (100 points)
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Instructions: Show adequate justification for each answer. The higher
of your two scores, between yesterday and today, will be recorded. |
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1. |
Please refer to the computer printout on p.
481 of the Barron’s book. A LSRL fit has been performed on miles per gallon
versus speed (miles per hour) for a new model automobile. |
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(a) |
Does the association between miles per
gallon and speed appear to be positive or negative? How can you tell? |
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(b) |
List (do not check) the assumptions needed
in order to test the hypothesis that the true correlation coefficient, when
all possible miles per gallon figures are plotted against all possible speeds
in this domain, is nonzero. |
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(c) |
Sketch an example of a residual plot that
does not satisfy the assumptions
needed in part (b). |
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(d) |
Find the value of the standard error of the
slope, sb1. |
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(e) |
Find the unadjusted linear correlation
coefficient. |
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(f) |
How many data points were used in this
analysis? |
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(g) |
The P-values
given are 2-tailed. Write a conclusion for the question posed in part (b),
assuming that all assumptions are met. |
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(h) |
Compute a 99% confidence interval for the true
slope of the LSRL. Show your work. |
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2. |
Explain, using several sentences, exactly
what you can conclude if the points on a residual plot for a LSRL all lie on a
straight line. Important: Also sketch that residual plot. |