Stats 60
Week 3 Extra Practice
1. The speed (miles per hour) and mileage (miles per gallon) of a certain car is shown below:
Speed
MPG
20
24
30
28
40
30
50
28
60
24
Sketch a scatterplot of these data. Does there seem to be a relationship between speed and
mileage? Then calculate the correlation coefficient. Explain the apparent contradiction.
2. A study of the log10 of income (in units of $1000) and years of education found the correlation
between log10 (Income in $1000’s) and years of education to be approximately 0.4. The average
log10 (Income in $1000’s) was 2.2 with an SD of 0.4. The average years of education was 14 with
an SD of 2.
(a) Predict the log10 (Income in $1000’s) of a student with 16 years of education.
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(b) Suppose a given person is in the 80th percentile of log10 (Income in $1000’s). Estimate the
percentile rank of the number of years of education of this person.
(c) What fraction of people with 16 years of education earn more than $100,000?
(Remember: log10 ($100,000 in $1000’s) = log10 (100) = 2.)
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3. A study found that average education levels in a sample of DINK (double income no kids) were
found to be 14 years for both husbands and wives each with an SD of 3 years. The correlation
was found to be 0.6.
(a) The average years of education for women of husbands with 16 years of education (give or
take a few months) was approximately 15.3 years. Is this consistent with the scatterplot
being football shaped?
(b) Would you expect the average years of education for husbands of women with 15.3 years of
education to be approximately 16 years?
4. If you haven’t done so already, complete Examples 1 and 3 from this week’s handout.
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