QA 233 (Basic Business Statistics)

Practice Problems II - Chapters 1-3

Hello QA 233 students! The following problems require you to use material from 'Introduction to Data and Statistics,' 'Descriptive Statistics: Organizing and Displaying Data,' and 'Descriptive Statistics: Numerical Measures' (slide sets 1-3 and chapters 1-3 in the ASW textbook). I have also posted the solutions on the QA 233 Virtual Classroom web page. Have a good day.

Mr. Mooney is the President of the Commerce Bank. He has asked his assistant, Miss Jane Hathaway, to collect data from a random sample of his bank’s clientele. Mr. Mooney asks Miss Hathaway to collect data on Age, Gender, Number Of Televisions Owned, 1999 State Income Tax, and Current Checking Account Balance. Consider the following data set (collected on January 12, 2000 by Miss Hathaway for Mr. Mooney) for each of the subsequent questions:

Age	Gender	Number of TV’s Owned	Income Tax	Account Balance
25	M	2	$1,295.23	$43.27
32	F	4	$4,904.01	$853.71
47	F	1	$3,488.81	$1739.22
26	M	5	$1,561.90	-$64.85
59	F	2	$1,391.24	$2255.77
34	M	4	$7,729.68	$597.71
73	F	10	$5,160.58	$1436.88
48	F	2	$3,052.49	$477.60

1. How many observations has Ms. Hathaway collected? On how many variables has she collected data? At what level is each variable measured?

 

2.  Please help Miss Hathaway by providing three measures of central location for Current Checking Account Balance. Which of these would you recommend that Miss Hathaway use? Why?

 

3. What is the 30% trimmed mean of Current Checking Account Balance for the sample in the previous problem?

 

4. Is this data time series or cross sectional in nature? Please explain your response.

 

5. Construct an appropriate graphical display of Number Of Television Sets Owned. Provide an interpretation of your display. Is this display useful? Why or why not?

 

6. Have these data been collected observationally or experimentally? Please explain your response.

 

7. Please help Miss Hathaway by providing four measures of dispersion for Current Checking Account Balance. Which of these would you recommend that Miss Hathaway use? Why?

 

8. Construct an appropriate graphical display that portrays the relationship between Age and Number Of Television Sets Owned. Provide an interpretation of your display. Also provide a numerical measurement of the strength of this relationship and interpret your result.

 

9. Please provide an appropriate summary measure for the values of Gender included in the data. Why is this measure appropriate?

 

10. Calculate the 23^rd, 58^th, and 81^st percentiles for Current Checking Account Balance.

 

11. Which variable, 1999 State Income Tax Or Current Checking Account Balance, is more disperse?

 

12. Provide and interpret a box plot for Current Checking Account Balance.

 

13. Construct displays of the values of Age, Number Of Televisions Owned, 1999 State Income Tax, and Current Checking Account Balance for each observation in the data set. Suggest one means by which you could augment your displays to incorporate information on the Gender of each observation.

 

14. If you are offered two potential investments, one that guarantees you a 45% return at the end of ten years and one that offers you an annual return of 4% for ten years. Which investment will yield the highest annual return?

 

15. Suppose you are considering two seven-year investments; one potential investment offers you 4.6% annual return for seven years, while the other guarantees you an 8% annual rate of return for the first three years of investment and a 3% annual rate of return for the last four years. Which investment will yield the highest annual rate of return?

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