# 15 Questions

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Several years ago, the state of California launched an aggressive advertisement campaign against smoking. We’re interested in the usefulness of this campaign among college students. We’ve interviewed students from
24college campuses in California and recorded for each campus the percentage of students who claimed that they had encountered at least one anti-smoking advertisement on campus in the past month. Our results are displayed in the following histogram:10
5
0
Frequency2
8
8
616
32
48
64
80
Percentage of studentsBased on this histogram, estimate the standard deviation of the sample of
24percentages.
Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.
(If necessary, consult a list of formulas.)Clears your work.

Ten years ago, a psychologist specializing in male-female relationships authored a book detailing the way in which he believed couples could improve their relationships. His publisher recently was interested in the effect the book has had on married men. The publisher interviewed
64married men and asked each to rate his marriage, on a scale of
1to
20, both before reading the book and after reading the book. For each man, the difference between the two ratings was recorded. These differences are summarized in the histogram below. Note that a negative difference means that the marriage rating before reading the book was higher than the marriage rating after.35
30
25
20
15
10
5
0
Frequency4
4
32
20
4-4
0
4
8
12
16
Difference in marriage ratingBased on this histogram, estimate the standard deviation of the sample of
64differences.
Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.

The manufacturer of Doze-Off sleeping pills claims that the standard deviation of the time it takes insomniacs to fall asleep after taking the pill is no more than
5minutes. To test this claim, a consumer group performed a study involving
24adults who complained of trouble falling asleep. For each adult, the time needed to fall asleep after taking Doze-Off was recorded. The results were reported via the following histogram:15
10
5
0
Frequency2
12
6
44
8
12
16
20
Time to fall asleep (in minutes)Based on this histogram, estimate the standard deviation of the sample of
24times.
Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.

The following is a list of 10 measurements.
57, 21, -48, -98, 80, -43, 21, -19, -45, 3Send data
to Excel
Suppose that these 10 measurements are respectively labeled
x
1,
x
2,
…,
x
10. (Thus,
57is labeled
x
1,
21is labeled
x
2, and so on.) Compute the following.+

49
S
=
i
1
10
x
i

The following is a list of 15 measurements.
22, -92, -82, -32, 91, -98, 57, 21, -48, -98, 80, -43, 21, -19, -45Send data
to Excel
Suppose that these 15 measurements are respectively labeled
x
1,
x
2,
…,
x
15. (Thus,
22is labeled
x
1,

92is labeled
x
2, and so on.) Compute the following.S
=
i
1
15
x
i

The following is a list of 13 measurements.
-92, -82, -32, 91, -98, 57, 21, -48, -98, 80, -43, 21, -19Send data
to Excel
Suppose that these 13 measurements are respectively labeled
x
1,
x
2,
…,
x
13. (Thus,

92is labeled
x
1,

82is labeled
x
2, and so on.) Compute the following.S
=
i
1
13
+
x
i
11

The following data are the ages (in years) of
19economics teachers in a school district.51, 26, 34, 44, 37, 52, 56, 60, 43, 55, 52, 45, 42, 28, 54, 33, 46, 32, 37Send data
to Excel
Using the tool provided, construct a box-and-whisker plot for the data.
ANSWER: 26, 34, 44, 52, 60

The following data are the grades of
17students on an algebra test.79, 64, 63, 89, 63, 91, 85, 69, 75, 71, 72, 84, 90, 65, 55, 83, 85Send data
to Excel
Using the tool provided, construct a box-and-whisker plot for the data.55
60
65
70
75
80
85
90
95
Score on algebra testClears your work.

The following data are the numbers of local channels available in
18cities.11, 12, 13, 29, 37, 19, 34, 25, 26, 19, 14, 15, 5, 35, 32, 31, 36, 17Send data
to Excel
Using the tool provided, construct a box-and-whisker plot for the data.

A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The
8outcomes are listed in the table below. Note that each outcome has the same probability.
For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. (If necessary, consult a list of formulas.)Outcomes
ProbabilityTTT
THH
HTH
HHH
THT
HTT
HHT
TTH
Events
A tail on each of the first two tossesA head on the first toss or the second toss (or both)A head on the last toss

Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both the number of births
xper one thousand people in the population and the female life expectancy
y(in years) are given. These data are displayed in the Figure 1 scatter plot. Also given are the products of the birthrates and female life expectancies for each of the twelve countries. (These products, written in the column labelled ”
xy,” may aid in calculations.)Birthrate, x
(number of births per 1000 pop.)
Female life expectancy, y
(in years)xy
30.5
64.21958.1
40.5
66.02673
27.3
73.01992.9
33.6
65.32194.08
13.0
72.9947.7
51.6
60.13101.16
26.4
74.31961.52
18.5
71.61324.6
45.8
58.62683.88
50.4
54.12726.64
14.4
74.71075.68
48.6
60.92959.74Send data
to Excelx
10
15
20
25
30
35
40
45
50
55
60
y
50
55
60
65
70
75
80
85
0Figure 1Answer the following. Carry your intermediate computations to at least four decimal places, and round your answer as specified below. (If necessary, consult a list of formulas.)What is the value of the slope of the least-squares regression line for these data? Round your answer to at least two decimal places.

The well-known psychologist Dr. Elbod has established what he calls his Generalized Anxiety Scale (GAS). The GAS, which is a scale from
0to
10, measures the “general anxiety” of an individual, with higher GAS scores corresponding to more anxiety. (Dr. Elbod’s assessment of anxiety is based on a variety of measurements, both physiological and psychological.)We’re interested in making predictions about individuals’ sleep behavior based on their GAS scores. The bivariate data below give the GAS score (denoted by
x) and the number of hours of sleep last night (denoted by
y) for each of the fifteen adults participating in a study. A scatter plot of the data is shown in Figure 1.GAS score, x
Sleep time, y
(in hours)
9.2
6.1
7.9
6.9
2.0
8.0
7.1
6.5
3.1
6.9
6.1
8.0
6.4
6.0
8.1
5.4
1.5
8.7
9.0
5.9
0.9
7.2
3.8
8.2
4.1
7.3
4.8
6.0
3.4
7.6Send data
to Excelx
2
4
6
8
10
y
5
6
7
8
9
10
0Figure 1The value of the sample correlation coefficient
rfor these data is approximately

0.706.Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.)What is the value of the slope of the least-squares regression line for these data? Round your answer to at least two decimal places.What is the value of the y-intercept of the least-squares regression line for these data? Round your answer to at least two decimal places.Clears your work.

We want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we’re given the data in the table below. These data detail the distance from the beach (
x, in miles) and the selling price (
y, in thousands of dollars) for each of a sample of fifteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Also given are the products of the distances from the beach and house prices for each of the fifteen houses. (These products, written in the column labelled ”
xy,” may aid in calculations.)Distance from the beach, x
(in miles)
Selling price, y
(in thousands of dollars)xy
6.6
269.21776.72
9.6
203.11949.76
7.4
305.72262.18
5.3
261.31384.89
5.3
212.31125.19
17.0
222.43780.8
11.9
195.72328.83
7.5
292.82196
12.1
235.62850.76
10.4
270.72815.28
15.0
263.53952.5
14.2
198.22814.44
7.7
231.41781.78
5.1
312.91595.79
8.0
241.31930.4Send data
to Excelx
5
10
15
20
y
150
200
250
300
350
0Figure 1Answer the following. Carry your intermediate computations to at least four decimal places, and round your answer as specified below. (If necessary, consult a list of formulas.)What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places.Clears your work.

A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The
8outcomes are listed in the table below. Note that each outcome has the same probability.
For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. (If necessary, consult a list of formulas.)Outcomes
ProbabilityTTT
HTT
THH
TTH
THT
HTH
HHT
HHH
Events

Suppose that the genders of the three children of a family are soon to be revealed. An outcome is represented by a string of the sort GBB (meaning the oldest child is a girl, the second oldest is a boy, and the youngest is a boy). The
8outcomes are listed in the table below. Note that each outcome has the same probability.
For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. (If necessary, consult a list of formulas.)Outcomes
ProbabilityBGB
BBG
BBB
GGB
GBG
GBB
BGG
GGG
Events
A boy on the first birth or the third birth (or both)More girls than boysA boy on the second birth

Suppose that the genders of the three children of a family are soon to be revealed. An outcome is represented by a string of the sort GBB (meaning the oldest child is a girl, the second oldest is a boy, and the youngest is a boy). The
8outcomes are listed in the table below. Note that each outcome has the same probability.
For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. (If necessary, consult a list of formulas.)Outcomes
ProbabilityBGB
BGG
GGB
BBG
BBB
GBB
GGG
GBG
Events
A girl on both the first and the last birthsTwo or more boysA girl on the first birth or the second birth (or both)Suppose that the genders of the three children of a family are soon to be revealed. An outcome is represented by a string of the sort GBB (meaning the oldest child is a girl, the second oldest is a boy, and the youngest is a boy). The
8outcomes are listed in the table below. Note that each outcome has the same probability.
For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. (If necessary, consult a list of formulas.)Outcomes
ProbabilityBGB
BGG
GGB
BBG
BBB
GBB
GGG
GBG
Events
A girl on both the first and the last birthsTwo or more boysA girl on the first birth or the second birth (or both)

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