1. Determine whether you would take a census or use a sampling to collect data for the study described below.
The most popular grocery store among the 55 employees of a company.
2. Toyota wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 40 customers and asks them about their level of satisfaction with the company.
What type of sampling is used?
3. Decide which method of data collection you would use to collect data for the study.
A study of the effect on the human digestive system of a popular soda made with less carbonation.
4. The graph to the right shows the responses to the question, "does global warming contribute to E1 Nino?"
Identify the level of measurement of the data listed on the horizontal axis in the graph.
5. Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits.
Minimum = 12, maximum = 56, 6 classes
6. Use the given frequency distribution to find the
a. Class width.
b. Class midpoints.
c. Class boundaries.
Tern perature(°F) Frequency
32 - 35 1
36 - 39 3
40 - 43 5
44 - 47 11
48 - 51 7
52 - 55 7
56 - 59 1
7. The data represent the time, in minutes, spent reading a political blog in a day. Construct a frequency distribution using 5 classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which class has the greatest frequency and which has the least frequency?
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15
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4
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1
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1
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1
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19
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17
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7
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10
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1
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15
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6
|
3
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11
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18
|
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14
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17
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3
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0
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7
|
Which class has the greatest frequency?
Which class has the greatest frequency?
8. The data set below contains information about the number of children of world leaders. Use the data to construct a frequency distribution using six classes and to create a frequency polygon.
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Data Table
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Number of Children
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|
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9
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13
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6
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0
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9
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17
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3
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10
|
|
10
|
14
|
14
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9
|
3
|
3
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13
|
3
|
|
8
|
16
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0
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16
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5
|
17
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15
|
14
|
|
4
|
14
|
15
|
15
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1
|
0
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6
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12
|
|
17
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6
|
13
|
8
|
7
|
7
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11
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5
|
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5
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6
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13
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|
|
|
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9. Use the dot plot to list the actual data entries. What is the minimum data entry?
10. Construct a scatter diagram using the data table to the right. This data is from a study comparing the amount of tar and carbon monoxide (CO) in cigarettes. Use tar for the horizontal scale and use carbon monoxide (CO) for the vertical scale. Determine whether there appears to be a relationship between cigarette tar and CO.
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Tar
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CO
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Tar
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Full CO
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data set Tar CO
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16
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15
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10
|
12
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2
|
3
|
|
15
|
14
|
8
|
11
|
9
|
9
|
|
1
|
1
|
11
|
12
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6
|
7
|
|
13
|
14
|
18
|
18
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16
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15
|
|
5
|
7
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13
|
14
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16
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16
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11. Consider a frequency distribution of scores on a 50-point test where a few students scored much lower than the majority of students. Match this distribution with one of the graphs shown below.
12. Find the mean, median, and mode of the data, if possible. If any of these measures cannot be found or a measure does not represent the center of the data, explain why.
A sample of seven admission test scores for a professional school are listed below.
10.7 10.2 11.7 11.4 10.2 10.2 10.9
13. Find the mean, median, and mode of the data, if possible. If any of these measures cannot be found or a measure does not represent the center of the data, explain why.
The typing speeds (in words per minute) for several stenographers are listed below.
240 215 120 165 136 120 170 180 220 150
14. Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown below.
44 51 11 91 76 36 64 37 43 72 54 62 36 74 51
72 37 29 39 61 47 63 36 41 22 37 51 46 85 14
To find the 10% trimmed mean of a data set, order the data, delete the lowest 10% of the entries and the highest 10% of the entries, and find the mean of the remaining entries. Complete parts (a) through (c).
a. Find the 10% trimmed mean for the data.
b. Compare the four measure of central tendency, including the midrange.
c. What is the benefit of using a trimmed mean versus using a mean found using all data entries?
15. Find the range of the data set.
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2
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3
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4
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Key: 2 I 3 = 23
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3
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2
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5
|
8
|
9
|
9
|
9
|
|
4
|
3
|
3
|
5
|
8
|
8
|
9
|
|
5
|
5
|
9
|
7
|
7
|
|
|
|
6
|
8
|
8
|
8
|
9
|
|
|
|
7
|
6
|
6
|
|
|
|
|
|
8
|
1
|
1
|
|
|
|
|
|
9
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1
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3
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4
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7
|
|
|
16. Researchers conducted experiments with trees. Listed below are weights (kg) of trees given no fertilizer and trees treated with fertilizer and irrigation. Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results. Does there appear to be a difference between the two standard deviations?
No treatment: 0.13 0.11 0.12 0.29 0.36
Fertilizer and irrigation: 0.95 1.53 0.63 0.84 1.91
17. From a sample with n = 36, the mean duration of a geyser's eruptions is 3.15 minutes and the standard deviation is 0.65 minutes. Using Chebychev's Theorem, determine at least how many of the eruptions lasted between 1.85 and 4.45 minutes.
18. The coefficient of variation CV describes the standard deviation as a percent of the mean. Because it has no units, you can use the coefficient of variation to compare data with different units. Find the coefficient of variation for each set. What can you conclude?
CV = Standard deviation/mean.100%
Data Table
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Heights
|
Weights
|
|
76
|
183
|
|
77
|
168
|
|
80
|
224
|
|
77
|
222
|
|
65
|
169
|
|
72
|
208
|
|
80
|
168
|
|
76
|
183
|
|
72
|
182
|
|
65
|
220
|
|
77
|
187
|
|
66
|
205
|
19. The English statistician Karl Pearson (1857-1936) introduced a formula for the skewness of a distribution.
p = 3(x' - median)/s
Most distribution have an index of skewness between -3 and 3. When P > 0 the data are skewed right. When P < 0 the data are skewed left. When P = 0 the data are symmetric. Calculate the coefficient of skewness for each distribution. Describe the shape of each.
20. Identify the sample space of the probability experiment and determine the number of outcomes in the sample space.
Randomly choosing an even number between 1 and 10, inclusive
21. Classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.
A study on a college campus shows that 77% of the students like rap music.
22. An individual stock is selected at random from the portfolio represented by the box-and-whisker plot shown to the right. Find the probability that the stock price is (a) less than $21, (b) between $21 an $57, and (c) $34 or more.
23. Determine whether the events E and F are independent or dependent. Justify your answer.
a. E: A person attaining a position as a professor.
F: The same person attaining a PhD.
b. E: A randomly selected person having a high GPA.
F: Another randomly selected person having a low GPA.
c. E: The rapid spread of a cocoa plant disease.
F: The price of chocolate.
24. The following histograms each represent binomial distributions. Each distribution has the same number of trials n but different probabilities of success p.
Match p = 0.3, p = 0.5, p = 0.6 with the correct graph.
25. Assume that police estimate that 16% of drivers do not wear their seatbelts. They set up a safety roadblock, stopping cars to check for seatbelt use. They stop 20 cars during the first hour.
a. Find the mean, variance, and standard deviation of the number of drivers expected not to be wearing seatbelts. Use the fact that the mean of a geometric distribution is μ = 1/P and the variance is σ2 = q/p2.
b. How many cars do they expect to stop before finding a driver whose seatbelt is not buckled?
26. Use the standard normal table to find the z-score that corresponds to the cumulative area 0.7517. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores.
27. Find the z-scores for which 97% of the distribution's area lies between -z and z.
28. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graph. If you cannot, explain why and use the binomial distribution to find the indicated probabilities.
Five percent of workers in a city use public transportation to get to work. You randomly select 273 workers and ask them if they use public transportation to get to work. Complete parts (a) through (d).
a. Find the probability that exactly 19 workers will say yes.
b. Find the probability that at least 9 workers will say yes.
c. Find the probability that fewer than 19 workers will say yes.
d. A transit authority offers discount rates to companies that have at least 30 employees who use public transportation to get to work. There are 549 employees in a company. What is the probability that the company will not get the discount?
Can the normal distribution be used to approximate the binomial distribution?