1. Consider the population of all students at your college. You want to learn about total monthly entertainment expenses for a student.
(a) Specify the population unit.
(b) Specify the variable of interest.
(c) Specify the statistical population.
2. Consider the population of persons living in Chicago. You want to learn about the proportion which are illegal aliens.
(a) Specify the population unit.
(b) Specify the variable of interest.
(c) Specify the statistical population.
3. A student is asked to estimate the mean height of all male students on campus. She decides to use the heights of members of the basketball team because they are conveniently printed in the game program.
(a) Identify the statistical population and the sample.
(b) Comment on the selection of the sample.
(c) How should a sample of males be selected?
4. A phone survey in 20084 of 1010 adults included a response to the number of leisure hours per week. Identify the population unit, statistical population, and sample.
(a) Specify the population unit.
(b) Specify the statistical population.
(c) Specify the sample.
5. Each year a local weekly newspaper gives out "Best of the City" awards in categories such as restaurant, deli, pastry shop, and so on. Readers are asked to fill in their favorites on a form enclosed in this free weekly paper and then send it to the publisher. The establishment receiving the most votes is declared the winner in its category. Identify the population and sample and comment on the representativeness of the sample.
(a) Identify the population and the sample.
(b) Comment on the selection of the sample.
6. Which of the following are anecdotal and which are based on sample?
(a) Out of 200 students questioned, 40 admitted they lied regularly.
(b) Bobbie says the produce at Market W is the freshest in the city.
(c) Out of 50 persons interviewed at a shopping mall, 18 had made a purchase that day.
6. Cities must find better ways to dispose of solid waste. According to the Environmental Protection Agency, the composition of the 254 million tons of solid municipal waste created in 2007 was
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Paper and paperboard
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32.7%
|
|
Yard waste
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12.8%
|
|
Food waste
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12.5%
|
|
Plastics
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12.1%
|
|
Metals
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8.2%
|
|
Other materials
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21.7%
|
(a) Determine the percentage of other materials in the solid waste. This category includes glass, wood, rubber, and so on.
(b) Create a Pareto chart.
(c) What percentage of the total solid waste is paper or paperboard? What percentage is from the top two categories? What percentage is from the top five categories?
8. Data from one campus dorm on the number of burglaries are collected each week of the semester. These data are to be grouped into the classes 0 - 1, 2 - 3, 3 - 5, 6 or more. Both endpoints included. Explain where a difficulty might arise.
2.12 A major West Coast power company surveyed 50 customers who were asked to respond to the statement, "People should rely mainly on themselves to solve problems caused by power outages" with one of the following responses.
1. Definitely agree
2. Somewhat agree
3. Somewhat disagree
4. Definitely disagree
The responses are as follows:
4 2 1 3 3 2 4 2 1 1 2 2 2 2 1 3 4
1 4 4 1 3 2 4 1 4 3 3 1 1 1 2 1 1
4 4 4 4 4 1 2 2 2 4 4 4 1 3 4 2
Construct a frequency table.
9. A sample of 50 departing airline passengers at the main check-in counter produced the following number of bags checked through to final destinations.
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0
|
1
|
2
|
2
|
1
|
2
|
1
|
2
|
3
|
0
|
1
|
0
|
|
1
|
1
|
0
|
1
|
3
|
0
|
1
|
2
|
1
|
1
|
1
|
2
|
|
1
|
2
|
2
|
1
|
2
|
0
|
0
|
2
|
2
|
1
|
1
|
1
|
|
1
|
1
|
1
|
1
|
2
|
0
|
1
|
3
|
0
|
1
|
2
|
1
|
|
1
|
3
|
|
|
|
|
|
|
|
|
|
|
(a) Make a relative frequency line diagram.
(b) Comment on the pattern.
(c) What proportion of passengers who check in at the main counter fail to check any bags?
10. A zoologist collected wild lizards in the Southwestern United States. Thirty lizards from the genus Phrynosoma were placed on a treadmill and their speed measured. The recorded speed (meters/second) is the fastest time to run a half meter. (Courtesy of K. Bonine.)
|
1.28
|
1.36
|
1.24
|
2.47
|
1.94
|
2.52
|
2.67
|
1.29
|
|
1.56
|
2.66
|
2.17
|
1.57
|
2.10
|
2.54
|
1.63
|
2.11
|
|
2.57
|
1.72
|
0.76
|
1.02
|
1.78
|
0.50
|
1.49
|
1.57
|
|
1.04
|
1.92
|
1.55
|
1.78
|
1.70
|
1.20
|
|
|
(a) Construct a frequency distribution using the class intervals 0.45-0.90, 0.90-1.35, and so on, with the endpoint convention that the left endpoint is included and the right endpoint is excluded. Calculate the relative frequencies.
(b) Make a histogram.
11. The following is a stem-and-leaf display with two-digit leaves. (The leading leaf digit = 10.0.)
1
2 46 68 93
3 19 44 71 82 97
4 05 26 43 90
5 04 68
6 13
List the corresponding measurements.
12. Calculate the mean and median for each of the following data sets.
(a) 2 5 1 4 3
(b) 26 30 38 32 26 31
(c) -1 2 0 1 4 -1 2
13. Old Faithful, the most famous geyser in Yellowstone Park, had the following durations (measured in seconds) in six consecutive eruptions:
240 248 113 268 117 253 Given
113 117 240 248 253 268 Put in order
(a) Find the sample median.
(b) Find the sample mean.
14. With reference to the water quality data in Exercise 2.17:
180 1600 90 140 50 260 400 90 380 110 10 60 20 340 80 Given
10 20 50 60 80 90 90 110 140 180 260 340 380 400 1600 In Order
(a) Find the sample median, first quartile, and third quartile.
(b) Find the sample 90th percentile.
15. With reference to the data on the length of 10 major league baseball games in Exercise 2.43:
167 211 187 176 170 158 198 218 145 232
(a) Find the sample mean.
(b) Find the sample variance.
(c) Find the sample standard deviation.
16. The following summary statistics were obtained from a data set.
Sample Mean = 80.5 q1 = 75.5
S = 10.5 q2 = 96.0
Median = 84.0
Approximately what proportion of the observations are:
(a) Below 96.0?
(b) Above 84.0?
(c) In the interval 59.5 to 101.5?
(d) In the interval 75.5 to 96.0?
(e) In the interval 49.0 to 112.0?
State which of your answers are based on the assumption of a bell-shaped distribution.