Document 6575237

AP Statistics
Mrs. Spano
Chapter 3
Name_________________________
Date__________________________
Practice
1. Each of the following statements contains an error. Explain what is wrong in each case.
(a) “There is a high correlation between the gender of American workers and their
income.”
(b) “We found a high correlation (r=1.09) between students’ ratings of faculty teaching
and ratings made by other faculty members.”
(c) The correlation between planting rate and yield of corn was found to be r = 0.23
bushel.”
2. You have data for many years on the average price of a barrel of oil and the average retail
price of a gallon of unleaded regular gasoline. If you want to see how well the price of
oil predicts the price of gas, then you would make a scatterplot with _____ as the
explanatory variable.
(a) The price of oil
(b) The price of gas
(c) The year
(d) Either oil price or gas price
(e) Time
3. In a scatterplot of the average price of a barrel of oil and the average retail price of a
gallon of gas, you expect to see
(a) Very little association
(b) A weak negative association
(c) A strong negative association
(d) A weak positive association
(e) A strong positive association
4. The graph below plots the gas mileage (mile per gallon) of various cars from the same
model year versus the weight of these cars in thousands of pounds. The points marked
with squares correspond to cars made in Japan. From this plot, we may conclude that
(a) There is a positive association between weight and gas mileage for Japanese cars.
(b) The correlation between weight and gas mileage for all cars is close to 1.
(c) There is little difference between Japanese cars and cars made in other countries.
(d) Japanese cars tend to be lighter in weight than other cars.
(e) Japanese cars tend to get worse gas mileage than other cars.
5. If women always married men who were 2 years older than themselves, what would the
correlation between the ages of husband and wife be?
(a) 2
(b) 1
(c) 0.5
(d) 0
(e) Can’t tell without seeing the data
6. The figure below is a scatterplot of reading test scores again IQ test scores for 14 fifthgrade children. There is one low outlier in the plot. The IQ and reading scores for this
child are
(a) IQ = 10, reading = 124
(b) IQ = 96, reading = 49
(c) IQ = 124, reading = 10
(d) IQ = 145, reading = 100
(e) IQ = 125, reading = 54
7. If we leave out the low outlier, the correlation for the remaining 13 points in the figure
above is closest to
(a) -0.95
(b) -0.5
(c) 0
(d) 0.5
(e) 0.95
8. The figure below is a scatterplot of reading test scores against IQ test scores for 14 fifthgrade children. The line is the least-squares regression line for predicting reading score
from IQ score. If another child in this class has IQ score 110, you predict the reading
score to be close to
(a) 50
(b) 60
(c) 70
(d) 80
(e) 90
9. The slope of the line in #8 is closest to
(a) -1
(b) 0
(c) 1
(d) 2
(e) 46
10. Smokers don’t live as long (on average) as nonsmokers, and heavy smokers don’t live as
long as light smokers. You perform least-squares regression on the age at death of a
large group of male smokers y and the number of packs per day they smoked x. The
slope of your regression line
(a) Will be greater than 0
(b) Will be less than 0
(c) Will be equal to 0
(d) You can’t perform regression on these data
(e) You can’t tell without seeing the data
For # 11 – 15, use the following: Measurements on young children in Mumbai,
India, found this least-squares line for predicting height y from arm span x:
yˆ = 6.4 + 0.93 x
11. How much does height increase on average for each additional centimeter of arm span?
(a) 0.93 cm
(b) 1.08 cm
(c) 5.81 cm
(d) 6.4 cm
(e) 7.33 cm
12. According to the regression line, the predicted height of a child with an arm span of
100cm is about
(a) 106.4 cm
(b) 99.4 cm
(c) 93 cm
(d) 15.7 cm
(e) 7.33 cm
13. By looking at the equation of the least-squares regression line, you can see that the
correlation between height and arm span is
(a) Greater than zero
(b) Less than zero
(c) 0.93
(d) 6.4
(e) Can’t tell without seeing the data
14. In addition to the regression line, the report on the Mumbai measurements says that
r 2 = 0.95 . This suggests that
(a) Although arm span and height are correlated, arm span does not predict height very
accurately.
(b) Height increases by 0.95 = 0.97 cm for each additional centimeter of arm span
(c) 95% of the relationship between height and arm span is accounted for by the
regression line.
(d) 95% of the variation in height is accounted for by the regression line.
(e) 95% of the height measurements are accounted for by the regression line.
15. One child in the Mumbai study had a height 59 cm and arm span 60 cm. This child’s
residual is
(a) -3.2 cm
(b) -2.2 cm
(c) -1.3 cm
(d) 3.2 cm
(e) 62.2 cm
Review Questions: Answer #16-18 on a separate piece of paper.
16. Here are the weights (in milligrams) of 58 diamonds from a nodule carried up to the
earth’s surface in surrounding rock. These data represent a single population of
diamonds formed in a single event deep in the earth.
13.8
10.9
7.6
5.4
1.4
4.0
3.7
9.0
9.0
5.1
0.1
2.3
33.8
9.0
9.5
5.3
4.7
4.5
11.8
14.4
7.7
3.8
1.5
27.0
6.5
7.6
2.1
2.0
18.9
7.3
3.2
2.1
0.1
19.3
5.6
6.5
4.7
0.1
20.8
18.5
5.4
3.7
1.6
25.4
1.1
7.2
3.8
3.5
23.1
11.2
7.8
4.9
3.7
7.8
7.0
3.5
2.4
2.6
Make a graph that shows the distribution of weights of these diamonds. Describe the
shape of the distribution and any outliers. Use numerical measures appropriate for the
shape to describe the center and spread.
17. A government report looked at the amount borrowed for college by students who
graduated in 2000 and had taken out student loans. The mean amount was
x = $17, 776 and the standard deviation was s x = $12, 034. The median was $15,532 and
the quartiles were Q1 = $9,900 and Q3 = $22,500.
(a) Compare the mean and the median. Also compare the distances of Q1 and Q3 from
the median. Explain why both comparisons suggest that the distribution is rightskewed.
(b) The right-skew pulls the standard deviation up. So a Normal distribution with the
same mean and standard deviation would have a third quartile larger than the actual
Q3. Find the third quartile of the Normal distribution with µ = $17, 776 and
σ = $12, 034 and compare it with Q3 = $22,500.
18. In its Fuel Economy Guide for 2008 model vehicles, the Environmental Protection
Agency gives data on 1152 vehicles. There are a number of outliers, mainly vehicles
with very poor gas mileage. If we ignore the outliers, however, the combined city and
highway gas mileage of the other 1120 or so vehicles is approximately Normal with a
mean 18.7 miles per gallon (mpg) and standard deviation 4.3 mpg.
(a) The 2008 Chevrolet Malibu with a four-cylinder engine has a combined gas mileage
of 25 mpg. What percent of all vehicles have worse gas mileage than the Malibu?
(b) How high must a 2008 vehicle’s gas mileage be in order to fall in the top 10% of all
vehicles? (The distribution omits a few high outliers, mainly hybrid gas-electric
vehicles.)