Question 1: The U.S. Government Accountability Office recently indicated the price of college textbooks has been rising an average of 6% annually since the academic year 1987-1988. The report estimated that the average cost of books and supplies for first-time students at four-year public universities for the academic year had reached $898. A data set that would produce this average follows:
537.51 1032.52 1119.17 877.27 856.87 739.91 963.76
847.92 1393.81 524.68 1012.91 1176.46 944.60 708.26
1074.35 778.78 967.91 562.55 789.50 1051.65
a) Calculate the mean and standard deviation.
b) Determine the number of standard deviations the most extreme cost is away from the mean. If you were to advise a prospective student concerning the money the student should save to afford the cost of books and supplies for at least 90% of colleges, determine the amount you would suggest. (Hint: Don't forget the yearly inflation of cost of books and supplies.)
Question 2: Wageweb.com exhibits salary data obtained from surveys. It provides compensation information on over 170 benchmark positions, including finance positions. It reports the salaries of chief finance officers for mid-size firms. Suppose that a sample is taken of the annual salaries for 25 CFOs. Assume the data are in thousands of dollars:
173.1 171.2 141.9 112.6 211.1 156.5 145.4 134.0 192.0
185.8 168.3 131.0 214.4 155.2 164.9 123.9 161.9 162.7
178.8 161.3 182.0 165.8 213.1 177.4 159.3
a) Calculate the mean salary of the CFOs.
b) Base on measures of the center of the data; determine if the CFO salary data are skewed.
c) Construct a box and whisker plot and summarize the characteristics of the CFO salaries that it reveals
Question 3: A country library in Minnesota reported the following number of books checked out in 15 randomly selected months:
5,176 6,005 5,052 5,310 4,188
4,132 5,736 5,381 4,983 4,423
5,002 4,573 4,209 5,611 4,568
Determine the range, variance, and standard deviation for sample data.
Question 4: Gold's Gym selected a random sample of 10 customers and monitored the number of times each customer used the workout facility in a one-month period. The following data were collected:
10 19 17 19 12 20 20 15 16 13
Gold's managers are considering a promotion in which they reward frequent users with a small gift. They have decided that they will only give gifts to those customers whose number of visits in a one-month period is 1 standard deviation above the mean. Find the minimum number of visits required receive a gift.
Question 5: Nielsen Monitor-Plus, a service of Nielsen Media Research, is one of the leaders in advertising information services in the United States , providing advertising activity for 16 media, including television tracking, in all 210 Designated Market Area (DMAs). One of the issues it has research is the increasing amount of "clutter"-nonprograming minutes in an hour of prime time including network and local commercials and advertisements for other shows. Recently it found the average nonprogramming minutes in an hour of prime-time broadcasting for network television was 15:48 minutes. For cable television, the average was 14:55 minutes.
a) Calculate the difference in the average clutter between network and cable television.
b) Suppose the standard deviation in the amount of clutter for both the network and cable television was either 5 minutes or 15 seconds. Which standard deviation would lead you to conclude that there was a major difference in the two clutter averages? Comment.
Question 6: Consider the following set of sample data:
78 121 143 88 110 107 62 122 130 95 78 139 89 125
a) Compute the mean and standard deviation for these sample data.
b) Calculate the coefficient of variation for these sample data and interpret its meaning
c) Using Tchebysheff's Theorem, determine the range of values that should include at least 89% of the data. Count the number of data values that fall into this range and comment on whether your interval range was conservative or not.
Question 7: Consider the following population:
71 89 65 97 46 52 99 41 62 88
73 50 91 71 52 86 92 60 70 91
73 98 56 80 70 63 55 61 40 95
a) Determine the mean and variance.
b) Determine the percentage of data values that fall in each of the following intervals:
x±2s,x±3s,x±4s
c) Compare these with the percentages specified by Tchebysheff theorem.
Question 8: Anaheim Human Resources, Inc., performs employment screenings for large companies in southern California. It usually follows a two-step process. First, potential applicants are given a test that covers basic knowledge and intelligence. If applicants score between a certain range, they are called in for a interview. If they score below a certain point, they are sent a rejection letter. If applicants score above a certain point, they are sent directly to client's human resources office without the interview. Recently, Anaheim Human Resources began working with a new client and formulated a new test just for this company. Thirty people were given the test, which is supposed to produce scores that are distributed according to a bell-shaped distribution. The following data reflect the scores of those 30 people:
76 75 74 56 61 76
62 96 68 62 78 76
84 67 60 96 77 59
67 81 66 71 69 65
58 77 82 75 76 67
Anaheim Human Resources has in the past issued a rejection letter with no interview to the lower 16% taking the test. They also send the upper 2.5% directly to the company without an interview. Based on the data the assumption of a bell-shaped distribution, what score should be used for the two cutoffs?