Lesson 4.2.1
4-40. Anthony has added a line of best fit to the scatter-plot at right. Do you agree with where he put
the line? Explain your reasoning.
[ Answers will vary. Possible response: The line should be placed slightly to the
lower left and a little less steep. ]
4-41. The choir is planning a trip to the water park and the parents are trying to determine how much to
charge each child. The cost to use a school bus is $350. Complete the table at right, graph your
results, then answer parts (a) and (b) below.
a. Think back to your work with proportions. Is this a proportional relationship?
b. Is there an association between the number of students and the cost per student? If so,
describe it considering the form, direction, and outliers.
[ See answers in table and answer graph below right.
a: No, it can never pass through (0, 0) ).
b: Non-linear negative association. The association is very strong—indeed, there is
no scatter at all in this relationship. There is a association because for every extra
student who goes on the trip, the cost decreases for all the students. It is a
negative association. ]
4-42. Westland Workers Union health and wellness department started a voluntary lunchtime weight
loss club. Members kept track of how much they ran each week for exercise, and how much weight
they lost over several weeks. Their data is in the table at right. Note that a negative weight loss is
actually a gain in weight.
a. Make a scatterplot of the data.
[ See solution graph below right. ]
b. Describe the association.
[ Positive linear association with one outlier. ]
c. Draw a line of best fit for the data. Find the equation of the line of best fit.
[ Disregarding the outlier, about y = 1.5x – 2. ]
d. Use the equation to predict the weight loss for an employee who ran 10 miles a week.
[ About 13 pounds. ]
e. Interpret the slope and y-intercept in context.
[ A slope of positive 1.5 means that for each additional mile run, we predict 1.5
pounds of weight loss; y-intercept of negative 2 means that a participant not
running at all expects to gain 2 pounds. ]
Lesson 4.2.2
4-48. At a family reunion, each family member recorded their age and their height.
a. Fully describe the association.
[ Moderate positive linear association with no outliers. ]
b. Copy the scatter-plot and draw the trend line. Does your y-intercept make sense in the context
of the problem?
[ If the y-intercept was drawn at the origin or negative, it does not make sense – a
child of zero years should have a little positive height. ]
4-49. Marissa’s older sister was discussing purchasing a car with her summer job earnings. Marissa
collected data from her friends at her job.
a. Marissa would like to know the typical age of her friends’ cars. What kind of a graphical display
should she use?
[ A box plot shows center and spread of one-variable numerical data nicely. ]
b. Marissa wants to convince her dad that newer cars are more fuel-efficient. What kind of
graph(s) should Marissa make to convince her dad?
[ A scatter-plot will show the relationship between age and mpg. ]
c. Make a scatterplot of the data.
[ See solution graph below. ]
d. Fully describe the association.
[ Strong negative linear association. ]
e. Draw a line of best fit on the data. Find the equation of the line of best fit.
[ Disregarding the outlier, about y = –3x+44 ]
f. Use the equation to predict what the correct mileage for a 4-year-old car should be.
[ About 32 mpg. ]
g. Interpret the slope and y-intercept in context.
[ A slope of negative 3 means that for each additional year old a car is, we expect
it to go 3 less miles per gallon; y-intercept of 44 means that a new car is predicted
to go 44mpg. ]
Lesson 4.2.3
4-53. An unusually severe increase in gasoline prices may have motivated car buyers to purchase a
highly fuel-efficient vehicle. Purchase behavior was collected in one state for one year and reported
below.
a. Complete the row and column totals. What is the dependent variable?
[ Fuel prices ]
b. Create a relative frequency table. Is there an association between fuel prices and
the number of highly fuel-efficient cars purchased?
[ There does not appear to be an association. See the relative frequency table
below. ]
4-54. Researchers have determined that teenagers’ memories are negatively affected by getting less than
10 hours of sleep. Being good scientists, the math students at North Middle School were skeptical, so
they did their own study. They asked 300 students to memorize 10 objects. The next day, each student
was asked how much sleep they got, and asked to list the ten items. The results are below. Make a
relative frequency table to determine if there is an association between hours of sleep and memory.
[ The dependent variable is the hours of sleep. There is an association. As the
number of hours of sleep increases, a higher percent of the students remember all
ten items. ]