Assignment
1. A major league baseball payrolls continue to escalate. Team payrolls in millions are as follows (USA Today Online Database March 2006).
|
Team
|
Payroll
|
Team
|
Payroll
|
|
Arizona
|
$ 62
|
Milwaukee
|
$ 40
|
|
Atlanta
|
86
|
Minnesota
|
56
|
|
Baltimore
|
74
|
N.Y. Mets
|
101
|
|
Boston
|
124
|
N.Y Yankees
|
208
|
|
Chi Club
|
87
|
Oakland
|
55
|
|
Chi White Sox
|
75
|
Philadelphia
|
96
|
|
Cincinnati
|
62
|
Pittsburgh
|
38
|
|
Cleveland
|
42
|
San Diego
|
63
|
|
Colorado
|
48
|
San Francisco
|
90
|
|
Detroit
|
69
|
Seattle
|
88
|
|
Florida
|
60
|
St. Louis
|
92
|
|
Houston
|
77
|
Tampa Bay
|
30
|
|
Kansas City
|
37
|
Texas
|
56
|
|
LA Angeles
|
98
|
Toronto
|
46
|
|
LA Dodgers
|
83
|
Washington
|
49
|
a. What is the media team payroll?
b. Provide a 5 number summary
c. Is the $208 million payroll for the New York Yankees an outlier? Explain.
2. Small business owners often look to payroll service companies to handle their employee payroll. Reasons are that small business owners face complicated tax regulations and penalties for employment tax errors are costly. According to the Internal Revenue Service, 26% of all small business employment tax returns contained errors that resulted in a tax penalty to the owner (The Wall Street Journal, January 30, 2006}. The tax penalty for a sample of 20 small business owners follows:
|
820
|
270
|
450
|
1010
|
890
|
700
|
1350
|
350
|
300
|
1200
|
|
390
|
730
|
2040
|
230
|
640
|
350
|
420
|
270
|
370
|
620
|
a. What is the mean tax for improperly filed employment tax returns?
b. What is the standard deviation?
c. Is the highest penalty, $2040, an outlier?
d. What are some of the advantages of a small business owner hiring a payroll service company to handle employee payroll services, including the employment tax returns?
3. Data on the 30 largest stock and balance funds provided on year and five year percentage returns for the period ending March 31, 2000 (The Wall Street Journal, April 10, 2000). Suppose we consider a one year return in excess of 50% to be high and a five year return in excess of 300% to be high. Nine of the funds had one year returns in excess of 50%, seven of the funds had five year returns in excess of 300%, and five year returns in excess of 300%
a. What is the probability of a high one year return and what is the probability of a high five year return?
b. What is the probability of both high one year returns and a high five year return?
c. What is the probability of neither a high one year return nor a high five year return?
4. The Dallas IRS auditing staff, concerned with identifying potentially fraudulent tax returns, believes that the probability of find a fraudulent return given that the return contains deductions for contributions exceeding the IRS standard is .20. Given that the deductions for contributions do not exceed the IRS standard for deductions due to contributions, what is the best estimate of the percentage of fraudulent returns?
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