1) The director of the West Arbor Senior Center decides to put together a database on the center’s activities. The center currently takes written records of services provided to clients, but the director feels that program information will be easier to access and analyze if the records are computerized. The program director generates the following sample data for 10 current clients:
Gender Home Delivery of Meals Assistance with Transportation
Male Yes Never
Female Yes Frequently
Female No Never
Male No Rarely
Female Yes Never
Male Yes Rarely
Male Yes Frequently
Female No Never
Male Yes Never
Female No Frequently
The director asks you to develop a measurement scheme and turn the data into numbers that can be put into a computerized database. Show the director how much you know about measurement, and develop a numerical coding scheme for each of the variables. Is a nominal-level coding scheme sufficient for all three variables? Explain.
2) The director of the Art Institute would like to present some data on the size of donations in this year’s annual report. He selects the following four categories to summarize donations.
Friends of the Institute ($25 to $99)
Silver Member ($100 to $249)
Gold Member ($250 to $499)
Platinum Member ($500 and above)
To get a sense of what the data will look like, the director gives you a sample of donations measured at the interval level and asks you to apply the coding scheme. Create an ordinal-level variable for donations using the data below.
3) The Mayor of a City feels that the productivity of meter butlers has declined in the past year. The mayor’s research assistant provides him with the accompanying data. Convert the frequency distributions to comparable distributions. What can you tell the Mayor about the productivity of meter butlers?
Number of Butlers
Parking Tickets Issued per Meter Butler May 2016 May 2017
21-30 5 6
31-40 7 9
41-50 9 12
51-60 5 7
61-70 3 1
4) The collective bargaining agreement between Family Services Agency and the Federation of Social Workers specifies that the average case load for caseworkers cannot exceed 45. Using the accompanying data, the agency claims compliance, yet the union argues that the agency has violated the agreement. Who is correct?
5) Complaints have reached the city manager of Normal that it is taking too long to pay bills submitted to the city. You are assigned to check how long it takes by looking at a few bills. Following are the lengths of time in days that it has taken the city to pay seven bills. Calculate mean, median, and standard deviation. Would you report the mean or the median? Explain.
34 27 64 31 30 26 35
6) The city manager of Grosse Our Pointe wants to make sure that pay raises are distributed fairly to all employees. He asks his assistant to gather data on raises for a random sample of police and fire employees, because he has received complaints that raises are not being distributed fairly in one of the departments.
X = 603 X=601
The assistant calculates the mean for each group of employees. He tells the city manager that because the average pay rise is just about the same in each department, there is really no fairness issue to worry about. If you were the city manager, would you accept these results, or would you ask the assistant to provide you with more information? Explain.
7) The civil service director for a municipality compiles the accompanying frequency distribution of scores on the civil service exam. Construct a cumulative frequency distribution and a cumulative frequency distribution chart.
Exam Score Number of Applicants
8) A manufacturer of computer chips claims that less than 10% of his products are defective. When 1,000 chips were drawn from a large production, 7.5% were found to be defective.
a. What is the population of interest?
b. What is the sample?
c. What is the parameter?
d. What is the statistic?
e. Does the value 10% refer to the parameter or to the statistic?
f. is the value 7.5% a parameter or a statistic?
g. Explain briefly how the statistic can be used to make inferences about the parameter to test the claim.
9) The placement office at a university regularly surveys the graduates 1 year after graduation and asks for the following information. For each, determine the type of data. a. What is your occupation?
b. What is your income?
c. What degree did you obtain?
d. What is the amount of your student loan?
e. How would you rate the quality of instruction? (excellent, very good, good, fair, poor)
10) [use file Xr02-27] Most universities have several different kinds of residences on campus. To help long-term planning, one university surveyed a sample of graduate students and asked them to report their marital status or relationship. The possible responses are:
The responses for a sample of 250 students were recorded and saved. Draw a graph that summarizes the information that you deem necessary.
11) [use file Xr02-48] The length (in inches) of 150 newborn babies were recorded. Use whichever graphical technique you judge suitable to describe these data. What have you learned from the graph?
12) [use file Xr02-64] How has the size of government changed? To help answer this question we recorded the U.S. federal budget receipts and outlays (billions of current dollars) for the year 1980 to 2005.
a) use a graphical technique to describe the size of the budget.
b) Calculate the budget deficits and graph these figures
c) Briefly describe what you have learned
13) [use file Xr02-82] In 2004, 4,456,000 men and 3,694,000 women were unemployed at some time during the year in the U.S. according to the Bureau of labor Statistics. A statistics practitioner wanted to investigate the reason for that unemployment status and whether the reasons differed by gender. A random sample of people 16 years of age and older was drawn. The reasons given for their status are:
1. Lost job
2. Left job
4. New Entrants
Determine whether there are differences between unemployed men and women in terms of the reasons for unemployment.
14) [use file Xr02-94] Are younger workers less likely to stay with their jobs? To help answer this question a random sample of workers was selected. Each was asked to report their age and how many months they have been employed with their current employer. Use a graphical technique to summarize these data.
15) [use file Xr03-08] Because Canada and the U.S. are the largest trading partners in the world, the exchange rate is vitally important. It is often the case that the difference between the two countries’ prime rate is a determinant in the exchange rate. An economist has recorded the monthly Canadian and American prime interest rates and the exchange rate (the value of one U.S. dollar in Canadian dollars) from 2000 to 2007.
a. draw a line chart of all three time series
b. What have you learned?
c. Can you improve the chart so that more information is derived? Explain. (Hint: is there a relationship between the difference in prime rates and the exchange rate?)
16) [use file Xr03-14] The following table shows school enrollment (in thousands) for public and private schools for the years 1990 to 2005.
a. Draw charts that allow you to claim that enrollment in private schools is “skyrocketing”
b. Draw charts that “prove” public school enrollment is stagnant
17) [use file Xr04-32] Many traffic experts argue that the most important factor in accidents is not the average speed of cars, but the amount of variation. Suppose that the speeds of a sample of 200 cars were taken over a stretch of highway that has seen numerous accidents. Compute the variance and standard deviation of the speeds, and interpret the results.
18) [use file Xr04-49] The Travel Industry Association of America sponsored a poll that asked a random sample of people how much they spent in preparation for pleasure travel. Determine the quartiles and describe what they tell you.