ES9 Additional Exercises

Chapter 1

1. Determine which of the following statements is descriptive in nature and which is inferential.

a. 99% of all big and tall travelers dislike cramped airline seating the most.

b. 99% of the 10,000 King-Size Co. customers dislike cramped airline seating the most.

2. The Design, Sample, and Method section of an article titled "Making Behavior Changes After a Myocardial Infarction" (Western Journal of Nursing Research, Aug. 1993) discusses the selection of 16 informants who constituted 8 family dyads. The article states that, "to initiate contact with informants, names of persons who met the criteria were obtained from the medical records of a cardiac rehabilitation center in central Texas. Potential informants were then contacted by telephone to obtain preliminary consent. Confidentiality and anonymity of informants were ensured by coding the data to identify informants and link dyads."

a. Is this a judgment sample or a probability sample?

b. Is it appropriate to perform statistical inference using this sample? Justify your answer.

3. The August 29/September 5, 1994 issue of U.S. News & World Report references a study by health economists at the University of Southern California that indicated that Alzheimer's disease cost the nation $82.7 billion a year in medical expenses and lost productivity. Patients' earning loss was $22 billion, the value of time of unpaid caregivers was $35 billion, and the cost of paid care was $24 billion.

a. What is the population?

b. What is the response variable?

c. What is the parameter?

d. What is the statistic?

4. A USA Snapshot from USA Today (Nov. 1, 1994) described the greatest sources of stress in starting a company. According to the snapshot, the CEOs of Inc. magazine's 500 fastest-growing private companies gave the following responses: 50% said company finances, 23% said the need to succeed, 10% said time commitments, 9% said personal relationships, and 8% were classified as "other." Would the data collected and used to determine these percentages be classified as qualitative or quantitative?

5. The June 1994 issue of Good Housekeeping reported on a study on rape. The study found that women who screamed, bit, kicked, or ran were more likely to avoid rape than women who tried pleading, crying, or offered no resistance, and they were no more apt to be injured. The authors, however, cautioned that the study could not be interpreted as proof that all women should forcefully resist. The study involved 150 Omaha, Nebraska, police reports of rape or attempted rape.

a. Are the data in this study attribute or numerical?

b. Is this a judgment or a probability sample?

Chapter 2

1. The USA Snapshot ® "How to say I love you" reports the results of a David Michaelson & Associates survey for Ethel M Chocolates, on the best way to show affection.

Best way to show affection Give gift Hold hands Hugging/kissing Smiling Other

Percent who said 10% 10% 51% 20% 9%

Draw a Pareto diagram picturing this information.

2. The January 10, 1991, USA Snapshot ® "What's in U.S. landfills" reports the percentages for each type of waste in our landfills: food-4%, glass-2%, metal-14%, paper-38%, plastic-18%, yard waste-11%, other-13%.

a. Construct a Pareto diagram displaying this information.

2. 
   Because of the size of the "other" category, the Pareto diagram may not be the best graph to use. Explain why, and describe what additional information is needed to make the Pareto diagram more appropriate.
   

3. The closing prices (nearest dollar) of the first 50 common stocks listed in the New York Stock Exchange with a value between $10 and $99 on July 23, 1998 was as follows:

26 72 26 58 16 65 13 22 45 48

13 24 31 17 52 12 17 31 11 52

75 37 36 35 12 75 38 32 14 54

52 90 57 22 21 28 25 52 27 43

Source: USA Today, July 23, 1998. p. 5B.

a. Construct a stem-and-leaf plot of these data.

b. Use the plot to determine the lowest and the highest stock price from those selected.

2. 
   What price interval defined by the plot contains the most values?
   

4. In the May 1990 issue of the journal Social Work, the following ungrouped frequency distribution was used to represent the "size of families":

Number of Children Number of Mexican-

Living at Home American Women

0 23

2 17

4 1

a. Which column represents the "size" of families? the "frequency" of those sizes?

b. Construct a frequency histogram of this distribution.

(Retain these answers for use in Exercise 2.21.)

5. All of the third-graders at Roth Elementary School were given a physical-fitness strength test. These data resulted:

12 22 6 9 2 9 5 9 3 5 16 1 22

18 6 12 21 23 9 10 24 21 17 11 18 19

17 5 14 16 19 19 18 3 4 21 16 20 15

14 17 4 5 22 12 15 18 20 8 10 13 20

6 9 2 17 15 9 4 15 14 19 3 24

a. Construct a dotplot.

b. Prepare a grouped frequency distribution using classes 1-4, 4-7, and so on, and draw a histogram of the distribution.

c. Prepare a grouped frequency distribution using classes 0-3, 3-6, 6-9, and so on, and draw a histogram of the distribution.

d. Prepare a grouped frequency distribution using class boundaries -2.5, 2.5, 7.5, 12.5 and so on, and draw a histogram of the distribution.

e. Prepare a grouped frequency distribution using classes of your choice, and draw a histogram of the distribution.

f. Describe the shape of the histogram found in (b), (c), (d), and (e) separately. Relate the distribution seen in the histogram to the distribution seen in the dotplot.

g. Discuss how the number of classes used and the choice of class boundaries used affect the appearance of the resulting histogram.

6. The following 40 amounts are the fees that Fast Delivery charged for delivering small freight items last Thursday afternoon.

4.03 3.56 3.10 6.04 5.62 3.16 2.93 3.82 4.30 3.86

4.57 3.59 4.57 5.16 2.88 5.02 5.46 3.87 6.81 4.91

3.62 3.62 3.80 3.70 4.15 4.07 3.77 5.77 7.86 4.63

4.81 2.86 5.02 5.24 4.02 5.44 4.65 3.89 4.00 2.99

a. Classify these data into a grouped frequency distribution.

2. 
   Construct a relative frequency histogram of these data.
   

7. An article titled "Financing Your Kids' College Education" (Farming, Sept./Oct. 1994) listed the following in-state tuition and fees per school year for 14 land-grant universities: 1554, 2291, 2084, 4443, 2884, 2478, 3087, 3708, 2510, 2055, 3000, 2052, 2550, 2013.

a. Find the mean in-state tuition and fees per school year.

b. Find the median in-state tuition and fees per school year.

c. Find the midrange in-state tuition and fees per school year.

2. 
   Find the mode, if one exists, per school year.
   

8. Atlantic Monthly (Nov. 1990) contains an article titled "The Case for More School Days." The number of days in the standard school year is given for several different countries as follows:

Japan 243 New Zealand 190

West Germany 226-240 Nigeria 190

South Korea 220 British Columbia 185

Israel 216 France 185

Luxembourg 216 Ontario 185

Soviet Union 211 Ireland 184

Netherlands 200 New Brunswick 182

Scotland 200 Quebec 180

Thailand 200 Spain 180

Hong Kong 195 Sweden 180

England/Wales 192 United States 180

Hungary 192 French Belgium 175

Swaziland 191 Flemish Belgium 160

Finland 190

a. Find the mean and median number of days per year of school for the countries listed. (Use the midpoint of the 226-240 interval for West Germany when computing your answers.)

b. Construct a stem-and-leaf display of these data.

c. Describe the relationship between the mean and the median and what properties of the data cause the mean to be larger than the median.

(Retain solution for use in answering Exercise 2.12.)

9. USA Today, July 22, 1998, reported the following statistics about the average in-season daily greens fees by state at US golf courses.

Highest: Hawaii, $85.70 Lowest: South Dakota, $23.80

a. Based on this information, find the "average" of the 50 state average fees.

2. 
   Explain why your answer in part (a) is the only average value you can determine from the given information.
   

10. USA Today, 10-28-94, reported on the average annual pay received by all workers covered by state and federal unemployment insurance for the 50 states. Connecticut had the highest with $33,169, South Dakota had the lowest with $18,613.

a. Estimate the national average with the midrange for the states.

b. The national average was reported to be $26,362. What can you conclude about the distribution of the state averages based on the relationship between the midrange and the national average?

11. An article titled "Financing Your Kids' College Education" (Farming, Sept./Oct. 1994) listed the following in-state tuition and fees per school year for 14 land-grant universities: 1554, 2291, 2084, 4443, 2884, 2478, 3087, 3708, 2510, 2055, 3000, 2052, 2550, 2013. Find the following:

a. variance s² b. standard deviation s

12 a. Find the range and the standard deviation for the number of days per year of school, using the data in Exercise 2.8.

b. Draw lines on the stem-and-leaf diagram drawn in answering Exercise 2.8 that represent the range and the standard deviation. Remember, the standard deviation is a measure for the mean.

c. Describe the relationship among the distribution of the data, the range, and the standard deviation.

13. A 1993 issue of Library Journal (Vol. 118, No. 17) gives the following table for the salaries of minority placements by type of library.

Library Type Number Average Salary

Academic 46 $27,825

Public 34 24,657

School 23 30,336

Special 16 29,406

Other 4 25,200

a. Find the total of all salaries for the above 123 individuals.

b. Find the mean salary for the above 123 individuals.

c. What is the modal library type? Explain.

2. 
   Find the standard deviation for the above 123 salaries.
   

14. A research study of manual dexterity involved determining the time required to complete a task. The time required for each of 40 disabled individuals is as follows (data are ranked):

7.1 7.2 7.2 7.6 7.6 7.9 8.1 8.1 8.1 8.3

8.3 8.4 8.4 8.9 9.0 9.0 9.1 9.1 9.1 9.1

9.4 9.6 9.9 10.1 10.1 10.1 10.2 10.3 10.5 10.7

11.0 11.1 11.2 11.2 11.2 12.0 13.6 14.7 14.9 15.5

Find:

a. Q₁ b. Q₂ c. Q₃ d. P₉₅

15. Consider the following set of ignition times that were recorded for a synthetic fabric.

30.1 30.1 30.2 30.5 31.0 31.1 31.2 31.3 31.3 31.4

31.5 31.6 31.6 32.0 32.4 32.5 33.0 33.0 33.0 33.5

34.0 34.5 34.5 35.0 35.0 35.6 36.0 36.5 36.9 37.0

37.5 37.5 37.6 38.0 39.5

Find:

a. the median b. the midrange c. the midquartile

16. In a study involving mastery learning (Research in Higher Education, Vol. 20, No. 4, 1984), 34 students took a pretest. The mean score was 11.04, and the standard deviation was 2.36. Find the z-score for scores of 9 and 15 on the 20-question pretest.

a. Find the limits within which at least 75% of the scores fell.

b. If the scores are normally distributed, what percentage of the scores will be below 30.16?

18. Below is a sample of one-way commute times, to the nearest minute, for 50 college students who are gainfully employed.

2 10 3 5 1 19 14 3 15 12

30 10 2 8 19 17 12 29 21 29

15 23 3 24 4 16 49 15 64 5

3 22 19 1 48 4 25 7 22 4

3 10 33 12 14 30 10 13 5 23

a. Construct three different kinds of graphs for this data.

b. Find the five measures of central tendency.

c. Find the three measures of dispersion.

d. Using one graph from part (a), one measure of central tendency from part (b) and one measure of dispersion from part (c), write a short presentation of the 50 data that you believe best describes the typical employed college student's commute to work.

e. Explain how the graph and the two statistics used in answering part (d) best describe the situation.

19. Compute the mean and the standard deviation for the following set of data. Then find the percentage of the data that is within two standard deviations of the mean.

1 | .4 .7 .1

2 | .4 .5

3 | .5 .0 .4 .1

4 | .4

6 | .8 .8 .2 .8 .6

7 | .5

8 |

20. Ask one of your instructors for a list of exam grades (15 to 25 grades) from a class.

a. Find five measures of central tendency.

b. Find the three measures of dispersion.

c. Construct a stem-and-leaf display. Does this diagram suggest that the grades are normally distributed?

d. Find the following measures of location: (1) Q₁ and Q₃, (2) P₁₅ and P₆₀, (3) the standard score z for the highest grade.

21. In the May 1990 issue of the journal Social Work, Marlow reports the following results:

Number of Children Mexican- Anglo-

Living at Home American Women American Women

0 23 38

2 17 15

Copyright 1990, National Association of Social Workers, Inc. Social Work.

a. Construct a frequency histogram for each of the preceding distributions. Draw them on the same axis, using two different colors, so that you can compare their distributions. (See Exercise 2.4.)

b. Calculate the mean and standard deviation for the Mexican-American data.

c. Calculate the mean and standard deviation for the Anglo-American data.

d. Do these two distributions seem to be different? Cite specific reasons for your answer.

22. Mutual funds attract millions of private investors every year. USA Today assembles a Mutual Fund Scoreboard that lists 15 of the largest stock funds available and a Mutual Fund Spotlight that shows the 14 top yielding growth and income funds during the past four weeks. Three more funds were selected randomly from the general listing of all mutual funds. Midway through 1998, the combined lists are shown below, together with each fund’s total return for the year:

a. Omit names and build a 4 x 8 table of ranked total return percentages in ascending order, reading vertically in each column.

b. Construct a 5-number summary table.

c. Find the midquartile total return percentage and the interquartile range.

d. What are the z-scores for Berkshire Capital Growth & Value, Income Fund of America, and Janus Fund?

e. Based on the data and your calculations, can you pinpoint the three funds selected at random?