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Chapter 8

AMS 5 Chapter Notes - Chapter 8: Scatter Plot, Senioritis

Applied Math and Statistics
Course Code
Yonatan Katznelson

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AMS 5 Practice 6
Chapter 8, #1, 2, 4, 5, 7, 10, 11
1. A study of the IQs of husbands and wives obtained the following results:
for husbands, average IQ = 100, SD = 15
for wives, average IQ = 100, SD = 15
r = .6
One of the following is a scatter diagram for the data. Which one? Say briefly why you
reject the others.
1) D, because (100, 100) is roughly in the middle of the oval and the oval contains points
outside of 1 SD.
2. (a) For a representative sample of cars, would the correlation between the age of the car
and its gasoline economy (miles per gallon) be positive or negative?
(b) The correlation between gasoline economy and income of owner turns out to be
positive. How do you account for this positive association?
2a) Negative, since unlike wine, mechanical parts don’t get better with age.
2b) More affluent people can afford cars with better gasoline economy cars.
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4. Is the correlation between the heights of husbands and wives in the U.S. around -.9, -.3, .
3, or .9? Explain briefly. (#3. Suppose men always married women who were exactly 8%
shorter. What would the correlation between their heights be?)
4) Assuming we’re going off of problem 3, it’d be .9 because of how close the values are.
5. Three data sets are collected, and the correlation coefficient is computed in each case.
The variables are…
(i) GPA in freshman year and in sophomore year
(ii) GPA in freshman year and in senior year
(iii) length and weight of two-by-four boards
Possible values for correlation coefficients are
-.50 0.0 0.30 0.60 0.95
Match the correlations with the data sets; two will be left over. Explain your choices.
(Note-Taker’s Note: There’s literally no data given, so I’m shooting in the dark and
basing my answers off my personal experiences; your answers may and should differ)
5i) 0.60, since a year difference (aside from classes) rarely affect one person’s work ethic
and they’ll usually perform about the same.
5ii) 0.0, since on one hand you could have someone in freshman year who suffered early
senioritis but buckled down in senior year in order to improve their chances of getting
into college, or the exact opposite, a studious freshman who lets themselves go in senior
year after losing all their hopes and dreams, or any number of odd cases that muddy the
correlation. Four years, especially during high school, is enough for anyone to change
5iii) .95, since factory standards are fairly strict in terms of weight and size of 2” x 4” boards
made of the same material.
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