Free Response Practice
1.
You are interested in how much time students spend on the Internet each day. Below you will find the data on the time spent on the
Internet (in minutes) for a particular day reported by a random sample of 30 students at a large high school:
7
42
72
2.
3.
20
43
75
24
44
77
25
45
78
25
46
79
28
47
83
28
48
87
30
48
88
32
50
135
35
41
151
a.
Are there any outliers? Justify your answer.
b.
Construct a modified boxplot.
c.
Would it be better to use the mean and standard deviation or the median and IQR to describe the center and spread of this
distribution? Why?
The army reports that the distribution of head circumference among male soldiers is approximately Normal with mean 22.8 inches and
standard deviation 1.1 inches.
a. A male soldier whose head circumference is 23.9 inches would be at what percentile?
b.
The army’s helmet supplier regularly stocks helmets that fit male soldiers with head circumferences between 20 and 26
inches. Anyone with a head circumference outside that interval requires a customized helmet order. What percent of male
soldiers require custom helmets?
c.
Find the interquartile range for the distribution of head circumference among male soldiers.
Elephants sometimes damage trees in Africa. It turns out that elephants dislike bees. They recognize beehives in areas where they are
common and avoid them. Can this be used to keep elephants away from trees? A group in Kenya placed active beehives in some trees
and empty beehives in others. Will elephant damage be less in trees with hives? Will empty hives keep elephants away? Researchers
want to design an experiment to answer these questions using 72 acacia trees.
a. Identify the experimental units, treatments, and the response variable.
b.
Describe how the researchers could carry out a completely randomized design for this experiment. Include a description of
how the treatments should be assigned.
4.
Three machines (A, B, C) are used to produce a large quantity of identical parts at a factory. Machine A produces 60% of the parts,
while Machines B and C produce 30% and 10% of the parts, respectively. Historical records indicate that 10% of the parts produced
by Machine A are defective, compared with 30% for Machine B and 40% for Machine C.
a. If we choose a part produced by one of these three machines, what’s the probability that it’s defective?
b.
5.
The U. S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park.
To assess public reaction, the service asks a random sample of 150 visitors if they favor the proposal. Of these, 89 say “Yes.”
a. Construct and interpret a 99% confidence interval for the proportion of all visitors to Yellowstone who favor the restrictions.
b.
6.
If a part is defective, what is the probability that it was produced by machine A?
Based on your work in part (a), can the U. S. Forest Service conclude that more than half of visitors to Yellowstone National
Park favor the proposal? Justify your answer.
The data below contains data from a random sample of 10 infants showing their intensity of their cry compared with their IQ at age
three.
Cry
IQ
10
87
12
97
18
109
12
119
20
132
16
136
a.
Find the least-squares regression line.
b.
Interpret the slope.
c.
Find and interpret the coefficient of determination.
d.
Find the residual for an infant whose cry intensity was 20.
33
159
19
103
13
104
18
112