Subject Code and Title / STAT 2000: Quantitative Analysis
Assessment / Module 1: Homework questions
Additional Information / When there is evidence of academic dishonesty, a student will face Misconduct Procedures. Please refer to Torrens policies and procedures in: http://www.torrens.edu.au/about/policies
Instructions / Answer these questions and problems
Chapter 1: Questions and problems
1, 5, 6, 7, 8, 11, 14, 16, 22, 30
1. Briefly explain why learning statistical inference is important for students of business and economics. Give two examples.
5. Suppose you are dealing with problems in probability and statistical inference. Which is usually the larger value in the problem, the population size or the sample size? Why?
6. State which type of statistical problem (deductive or inductive) each of the following assumptions makes.
(a) You know what the population characteristics are.
(b) You know what the sample characteristics are.
7. When a cosmetic manufacturer tests the market to determine how many women will buy eyeliner that has been tested for safety without subjecting animals to injury, is it involved in a descriptive statistics problem or an inferential statistics problem? Explain your answer.
8. As controller of the Hamby Corporation, you are directed by the chairman of the board to investigate the problem of overspending by employees who have expense accounts. You ask the accounting department to provide you with records of the number of dollars spent by each of 25 top employees during the past month. The following record is provided:
$292435
322
712
560 / $494
870
397
520
298 / $600
725
390
575
472 / $807
299
420
670
905 / $535
602
469
723
305
The question the board of directors wanted to be answered is “How many of our 25 top executives spent more than $600 last month?” What will be your answer? Are you dealing with descriptive statistics or inferential statistics?
11. Suppose the teacher in question 10 would like to predict the average grade of all her students by using only the midterm scores from one class. Should she use inferential or descriptive statistics?
14. Explain whether each of the following was arrived at via descriptive or inferential statistics.
(a) Ted Williams’ lifetime batting average
(b) The number of people watching the Super Bowl, based on A. C. Nielsen’s ratings
(c) The number of people who favour teacher-led prayer in school, based on a survey of churchgoers
(d) The average rate of return for IBM stock over the last 10 years
16. A popular commercial claims that “Four out of five dentists prefer sugarless gum.” Is this conclusion drawn from a sample or a population?
22. The following list gives the seven highest-paid baseball players for 1992 and their salaries.
Dwight Gooden / $5,166,666George Brett / 4,700,000
Roger Clemens / 4,300,000
Will Clark / 4,250,000
Andy Van Slyke / 4,250,000
Darryl Strawberry / 4,050,000
Fred McGriff / 4,000,000
(a) Does this list represent a sample or population of baseball players’ salaries?
(b) If you were the agent for a top baseball star, how could you use the foregoing information?
30. Refer to Table 2.2, in which annual macroeconomic data including GDP, CPI, 3-month T-bill rate, prime rate, private consumption, private investment, net exports, and government expenditures from 1960 to 2009 are given. Answer the following questions.
(a) How many observations are in the data set?
(b) How many variables are in the data set?
Chapter 2: Questions and problems
9, 14, 17, 19, 21
9. Use the following data from in table 2.2 to draw line charts for the following:
(a) GDP
(b) CPI
(c) GDP and CPI
(d) 3-month T-bill rate and prime rate
Table 2.2: Annual macroeconomic data 1960-2009 (in 2005 dollars)
Year / GDPa / CPIb / 3-monthT-bill rate / Prime
Rate / Private
consumption / Private
Investment / Net
exports / Government
expenditures
1960 / 2,830.9 / 29.585 / 2.88 / 4.82 / 1,784.4 / 296.5 / 111.5 / 111.5
1961 / 2,896.9 / 29.902 / 2.35 / 4.50 / 1,832.3 / 204.6 / 119.5 / 119.5
1962 / 3,072.4 / 30.253 / 2.77 / 4.50 / 1,911.1 / 332.0 / 130.1 / 130.1
1963 / 3,206.7 / 30.633 / 3.16 / 4.50 / 1,989.9 / 354.3 / 136.4 / 136.4
1964 / 3,392.3 / 31.038 / 3.55 / 4.50 / 2,108.4 / 383.5 / 134.2 / 134.2
1965 / 3,610.1 / 31.528 / 3.95 / 4.54 / 2,241.8 / 437.3 / 151.4 / 151.4
1966 / 3,845.3 / 32.417 / 4.86 / 5.63 / 2,369.0 / 475.8 / 171.6 / 171.6
1967 / 3,942.5 / 33.375 / 4.31 / 5.63 / 2,440.0 / 454.1 / 192.5 / 192.5
1968 / 4,133.4 / 34.792 / 5.34 / 6.31 / 2,580.7 / 480.5 / 209.3 / 209.3
1969 / 4,261.8 / 36.683 / 6.67 / 7.95 / 2,677.4 / 508.5 / 221.4 / 221.4
1970 / 4,269.9 / 38.842 / 6.39 / 7.91 / 2,740.2 / 475.1 / 233.7 / 233.7
1971 / 4,413.3 / 40.483 / 4.33 / 5.72 / 2,844.6 / 529.3 / 246.4 / 246.4
1972 / 4,647.7 / 41.808 / 4.07 / 5.25 / 3,019.5 / 591.9 / 263.4 / 263.4
1973 / 4,917.0 / 44.425 / 7.03 / 8.02 / 3,169.1 / 661.3 / 281.7 / 281.7
1974 / 4,889.9 / 49.317 / 7.83 / 10.08 / 3,142.8 / 612.6 / 317.9 / 317.9
1975 / 4,879.5 / 53.825 / 5.78 / 7.86 / 3,214.1 / 504.1 / 357.7 / 357.7
1976 / 5,141.3 / 56.933 / 4.97 / 6.84 / 3,393.1 / 605.9 / 383.0 / 383.0
1977 / 5,377.7 / 60.617 / 5.27 / 6.82 / 3,535.9 / 697.4 / 414.1 / 414.1
1978 / 5,677.6 / 65.242 / 7.19 / 9.06 / 3,691.8 / 781.5 / 453.6 / 453.6
1979 / 5,855.0 / 72.583 / 10.07 / 12.67 / 3,779.5 / 806.4 / 500.7 / 500.7
1980 / 5,839.0 / 82.383 / 11.43 / 15.27 / 3,766.2 / 717.9 / 566.1 / 566.1
1981 / 5,987.2 / 90.933 / 14.03 / 18.87 / 3,823.3 / 782.4 / 627.5 / 627.5
1982 / 5,870.2 / 96.533 / 10.61 / 14.86 / 3,876.7 / 672.8 / 680.4 / 680.4
1983 / 6,136.2 / 99.583 / 8.61 / 10.79 / 4,098.3 / 735.5 / 733.4 / 733.4
1984 / 6,577.1 / 103.933 / 9.52 / 12.04 / 4,315.6 / 952.1 / 796.9 / 796.9
1985 / 6,849.3 / 107.600 / 7.48 / 9.93 / 4,540.4 / 943.3 / 878.9 / 878.9
1986 / 7,089.5 / 109.692 / 5.98 / 8.33 / 4,724.5 / 936.9 / 949.3 / 949.3
1987 / 7,313.3 / 113.933 / 5.78 / 8.20 / 4,870.3 / 965.7 / 999.4 / 999.4
1988 / 7,613.9 / 118.275 / 6.67 / 9.32 / 5,066.6 / 988.5 / 1,038.9 / 1,038.9
1989 / 7,885.9 / 123.942 / 8.11 / 10.87 / 5,209.9 / 1,028.1 / 1,100.6 / 1,100.6
1990 / 8,033.9 / 130.658 / 7.49 / 10.01 / 5,316.2 / 993.5 / 1,181.7 / 1,181.7
1991 / 8,015.1 / 136.167 / 5.38 / 8.46 / 5,324.2 / 912.7 / 1,236.1 / 1,236.1
1992 / 8,287.1 / 140.308 / 3.43 / 6.25 / 5,505.7 / 986.7 / 1,273.5 / 1,273.5
1993 / 8,523.4 / 144.475 / 3.00 / 6.00 / 5,701.2 / 1,074.8 / 1,294.8 / 1,294.8
1994 / 8,870.7 / 148.225 / 4.25 / 7.14 / 5,918.9 / 1,220.9 / 1,329.8 / 1,329.8
1995 / 9,093.7 / 152.383 / 5.49 / 8.83 / 6,079.0 / 1,258.9 / -98.8 / 1,374.0
1996 / 9,433.9 / 156.858 / 5.01 / 8.27 / 6,291.2 / 1,370.3 / -110.7 / 1,421.0
1997 / 9,854.3 / 160.525 / 5.06 / 8.44 / 6,523.4 / 1,540.8 / -139.8 / 1,474.4
1998 / 10,283.5 / 163.008 / 4.78 / 8.35 / 6,865.5 / 1,695.1 / -252.6 / 1,526.1
1999 / 10,779.8 / 166.583 / 4.64 / 7.99 / 7,240.9 / 1,844.3 / -356.6 / 1,631.3
2000 / 11,226.0 / 172.192 / 5.82 / 9.23 / 7,608.1 / 1,970.3 / -451.6 / 1,731.0
2001 / 11,347.2 / 177.042 / 3.39 / 6.92 / 7,813.9 / 1,831.9 / -472.1 / 1,846.4
2002 / 11,553.0 / 179.867 / 1.60 / 4.68 / 8,021.9 / 1,807.0 / -548.8 / 1,983.3
2003 / 11,840.7 / 184.000 / 1.01 / 4.12 / 8,247.6 / 1,871.6 / -603.9 / 2,112.6
2004 / 12,263.8 / 188.908 / 1.37 / 4.34 / 8,532.7 / 2,058.2 / -688.0 / 2,232.8
2005 / 12,638.4 / 195.267 / 3.15 / 6.19 / 8,819.0 / 2,172.2 / -722.7 / 2,369.9
2006 / 12,976.2 / 201.550 / 4.73 / 7.69 / 9,073.5 / 2,230.4 / -729.2 / 2,518.4
2007 / 13,254.1 / 207.335 / 4.35 / 8.05 / 9,313.9 / 2,146.2 / -647.7 / 2,676.5
2008 / 13,312.2 / 215.214 / 1.37 / 5.09 / 9,290.9 / 1,989.4 / -494.3 / 2,883.2
2009 / 12,988.7 / 214.549 / 0.15 / 3.25 / 9,237.3 / 1,522.8 / -353.8 / 2,933.3
Source: Department of Commerce (Bureau of Economic Analysis), Economic Report of the President, February 2010
a Billions of 2005 dollars b CPI base: 1982-1984 = 100
14. You are given the following information about a certain company’s current assets over the past 4 years:
YearsCurrent assets / 1988 / 1989 / 1990 / 1991
Cash and marketable securities / 4,215 / 5,341 / 6,325 / 5,842
Receivables / 6,327 / 6,527 / 7,725 / 6,750
Inventories / 9,254 / 9,04 / 10,104 / 11,100
Other current assets / 2,153 / 3,277 / 4,331 / 3,956
Use a component-lines graph to plot this firm’s current assets.
17. A statistics teacher has given the following numbers of the traditional grades to her class of 105 students:
Number of students / Grade10 / A
30 / B
50 / C
10 / D
5 / E
(a) Use a bar graph to show the distribution of grades.
(b) Use a pie chart to show the distribution of grades.
(c) Which of these graphs do you think is best for presenting the distribution of grades? Why?
19. The following table gives the sales figures for five products manufactured by Trends Clothing Company, your employer.
Item / Sales (million $)Sweaters / 5
Shirts / 12
Pants / 9
Blazers / 16
Overcoats / 7
The president of the company asks you for a report showing how sales are distributed among the five goods. What type of chart would you use?
21. In the course of researching the benefits of diversification, you collect the information given in the table on portfolio returns, which presents rates of return for different portfolios.
(a) Use a line chart to plot the 20-year return for all five portfolios.
(b) What information do these plots provide?
Table 1: Portfolio returns
Year / Stocksa / Bondsb / 60 % stocks40 % bonds / 1/3 stocks
1/3 bonds
1/3 cash / BB&K
Indexc
1970 / 4.01% / 12.10 % / 7.52 % / 7.98 % / 4.7 %
1971 / 14.31 / 13.23 / 14.14 / 10.83 / 13.7
1972 / 18.98 / 5.68 / 13.54 / 9.38 / 15.1
1973 / 14.66 / _1.11 / _9.11 / _3.03 / _2.2
1974 / _26.47 / 4.35 / _14.88 / _5.44 / _6.6
1975 / 37.20 / 9.19 / 25.65 / 17.04 / 19.6
1976 / 23.84 / 16.75 / 21.18 / 15.19 / 11.5
1977 / _7.18 / _.67 / _4.57 / _0.94 / 6.1
1978 / 6.56 / _1.16 / 3.65 / 4.40 / 13.0
1979 / 18.44 / _1.22 / 10.28 / 9.14 / 11.5
1980 / 32.42 / _3.95 / 17.45 / 13.17 1 / 7.9
1981 / _4.91 / 1.85 / _1.99 / 4.06 / 6.4
1982 / 21.41 / 40.35 / 28.98 / 23.97 / 14.4
1983 / 22.51 / .68 / 13.43 / 10.52 / 15.4
1984 / 6.27 / 15.43 / 10.11 / 10.75 / 10.4
1985 / 32.16 / 30.97 / 31.85 / 23.38 / 25.4
1986 / 18.47 / 24.44 / 21.11 / 16.61 / 23.3
1987 / 5.23 / _2.69 / 3.59 / 3.92 / 8.6
1988 / 16.81 / 9.67 / 13.97 / 11.01 / 13.2
1989 / 31.49 / 18.11 / 26.24 / 19.22 / 14.3
Compound annual return / 11.55 / 9.00 / 10.89 / 9.78 / 11.54
Source: Bailard, Biehl & Kaiser, Ibbotson Associates. Inc. This figure was printed in the Wall
Street Journal on January 25, 1990, p. Cl
aStandard & Poor’s 500 index
bLong-term Treasury bonds
c20 % US stocks, 20 % bonds, 20 % cash, 20 % real estate, 20 % foreign stocks
Chapter 3: Questions and problems
9, 10, 12
9. On November 17, 1991, the Home News of central New Jersey used the bar chart given here to show that foreign investors are taxed at a lower rate than the US citizens.
(a) Construct a table to show frequency, relative frequency, and cumulative frequency.
(b) Draw a frequency polygon and a cumulative frequency polygon.
10. Use the EPS and DPS data given in Table 2.3 in Chapter 2 to construct frequency distributions.
Table 2.3: EPS, DPS and PPS for Johnson & Johnson, Merck, and S&P500
Year / Johnson & Johnson / Merck / S&P500DPS / EPS / PPS / DPS / EPS / PPS / PPS
1988 / 1.89 / 5.63 / 85.13 / 1.37 / 3.02 / 57.7 / 265.79
1989 / 1.1 / 3.19 / 59.38 / 1.7 / 3.74 / 77.5 / 322.84
1990 / 1.29 / 3.38 / 71.75 / 2 / 4.51 / 89.88 / 334.59
1991 / 1.51 / 4.3 / 114.5 / 2.34 / 5.39 / 166.5 / 376.18
1992 / 0.88 / 1.54 / 50.5 / 0.95 / 1.7 / 43.38 / 415.74
1993 / 1 / 2.71 / 44.88 / 1.06 / 1.86 / 34.38 / 451.41
1994 / 1.12 / 3.08 / 54.75 / 1.15 / 2.35 / 38.13 / 460.42
1995 / 1.25 / 3.65 / 85.5 / 1.24 / 2.63 / 65.63 / 541.72
1996 / 0.72 / 2.12 / 49.75 / 1.44 / 3.12 / 79.63 / 670.5
1997 / 0.83 / 2.41 / 65.88 / 1.7 / 3.74 / 106 / 873.43
1998 / 0.95 / 2.23 / 83.88 / 1.93 / 4.3 / 147.5 / 1085.5
1999 / 1.04 / 2.94 / 93.25 / 1.09 / 2.45 / 67.19 / 1327.33
2000 / 1.22 / 3.39 / 105.06 / 1.23 / 2.9 / 93.63 / 1427.22
2001 / 0.66 / 1.83 / 59.1 / 1.36 / 3.14 / 58.8 / 1194.18
2002 / 0.78 / 2.16 / 53.71 / 1.41 / 3.14 / 56.61 / 993.94
2003 / 0.91 / 2.39 / 51.66 / 1.45 / 3.03 / 46.2 / 965.23
2004 / 1.08 / 2.83 / 63.42 / 1.5 / 2.61 / 32.14 / 1130.65
2005 / 1.26 / 3.46 / 60.1 / 1.52 / 2.1 / 31.81 / 1207.23
2006 / 1.44 / 3.73 / 66.02 / 1.52 / 2.03 / 43.6 / 1310.46
2007 / 1.6 / 3.63 / 66.7 / 1.51 / 1.49 / 58.11 / 1477.19
2008 / 1.77 / 4.57 / 59.83 / 1.52 / 3.64 / 30.4 / 1220.04
2009 / 1.91 / 4.4 / 64.41 / 1.58 / 5.68 / 36.54 / 948.05
Source: Standard and Poor’s Compustat, Wharton Research Data Services (WRDS)
12. On November 17, 1991, the Home News of central New Jersey used the bar chart in the accompanying figure to show the 1980–1991 passenger traffic trends for Newark International Airport.