Problems

1. Table P1 repeats the falling body data from Checkpoint 2. Do these data agree or disagree with what you think should happen to a falling object? If there are discrepancies with what you think should happen, how do you think those discrepancies might arise in the process of data gathering?
   
   
   Table P1   Falling body data

   Time (seconds)	Distance (centimeters)		Time (seconds)	Distance (centimeters)
   0.16	12.1		0.57	150.2
   0.24	29.8		0.61	182.2
   0.25	32.7		0.61	189.4
   0.30	42.8		0.68	220.4
   0.30	44.2		0.72	254.0
   0.32	55.8		0.72	261.0
   0.36	63.5		0.83	334.6
   0.36	65.1		0.88	375.5
   0.50	124.6		0.89	399.1
   0.50	129.7

Most of the remaining problems require graph paper. Click on the image at the right to open a PDF file from which you can print your own graph paper. Start each exercise by labeling and scaling your axes in a way that is reasonable for that exercise. Use a full sheet of graph paper for each problem. (You may save the PDF file for future use.)

For Problems 2-12, do the following:

1. Make a scatter plot of the data in the given table.
2. Describe the shape of the graph.
3. Explain what the shape of the graph indicates about the relationship between the variables.

2. 
   

   Table P2   Related variables

   `x`	0.8	1.5	3.2	2.6	1.9	2.4	3.5	0.6	2.1
   `y`	0.7	2.1	10.5	6.8	3.5	5.9	12.4	0.3	4.3

3. 
   

   Table P3   Distance traveled by a falling object

   Time (seconds)	1	2	3	4	5	6	7	8	9	10
   Distance (meters)	5	19	44	78	123	176	240	313	396	489

4. 
   

   Table P4   Parcel Post Local Rates

   Weight Not Over (pounds)	1	2	3	4	5	6	7	8	9	10
   Postage (US dollars)	4.38	4.72	5.05	5.35	5.63	5.88	6.02	6.12	6.23	6.33

5. 
   

   Table P5   Temperature and pressure of a gas in a closed container

   Temperature (°K)	263	268	278	293	298	303	308	313	323
   Pressure (mm Hg)	752	755	777	811	834	840	854	892	906

6. 
   

   Table P6   Exports to Mexico from the United States
   Source: R. H. Ojeda et al., "North American Integration
   Three Years After NAFTA," UCLA, 1996

   Year	1987	1988	1989	1990	1991	1992	1993	1994	1995	1996
   Exports (billions of dollars)	20.49	20.55	22.84	26.84	42.69	46.20	51.89	60.88	79.54	90.94

7. 
   

   Table P7   Imports from Mexico to the United States
   Source: R. H. Ojeda et al., "North American Integration
   Three Years After NAFTA," UCLA, 1996

   Year	1987	1988	1989	1990	1991	1992	1993	1994	1995	1996
   Imports (billions of dollars)	13.31	20.27	25.44	31.27	49.97	62.13	65.37	79.35	72.45	82.68

8. 
   

   Table P8   Victims of Murder by Firearms in the U. S.
   Source: FBI, "Crime in the United States 2002"

   Year	1998	1999	2000	2001	2002
   Victims	9,220	8,480	8,661	8,890	9,369

9. 
   

   Table P9   Monthly ATM Transactions in the United States
   Source: Congressional Budget Office, "The market for ATM Services," Chapter II in
   COMPETITION IN ATM MARKETS: ARE ATMs MONEY MACHINES?, July, 1998

   Year	1988	1989	1990	1991	1992	1993	1994	1995	1996	1997
   ATM Transactions (millions)	373.4	426.4	479.3	534.9	600.5	642.1	704.5	807.4	890.3	915.0

10. 
    

    Table P10   Monthly Point-of-Sale Debit Card Transactions in the United States
    Source: Congressional Budget Office, "The market for ATM Services," Chapter II in
    COMPETITION IN ATM MARKETS: ARE ATMs MONEY MACHINES?, July, 1998

    Year	1988	1989	1990	1991	1992	1993	1994	1995	1996	1997
    POS Transactions (millions)	7.4	9.2	12.4	17.6	23.3	32.2	45.9	57.0	75.4	120.2

11. 
    

    Table P11   Average Player Salaries for the New York Yankees
    Source: ESPN, "Average Salaries from 1998-2005"

    Year	1998	1999	2000	2001	2002	2003	2004	2005
    Avg. Salary (millions of dollars)	2.229	3.216	3.656	3.930	4.903	4.687	6.382	7.391

12. 
    

    Table P12  Average Player Salaries for the Pittsburgh Pirates
    Source: ESPN, "Average Salaries from 1998-2005"

    Year	1998	1999	2000	2001	2002	2003	2004	2005
    Avg. Salary (millions of dollars)	0.460	0.714	1.004	1.292	1.370	1.159	0.917	0.964

13. Use the data in Tables P9 and P10 to construct a table of ratios of ATM transactions to POS transactions over the years 1988 to 1997. Make a scatter plot of the information in your new table. What is the shape of the graph? What conclusions (if any) can you draw about relative growth rates of ATM and POS transactions?
14. Make a scatter plot to analyze the relationship between rebounds and assists for the basketball data provided in Tables 2, 3, and 4. Use the graph to comment on important characteristics of the relationship.
    
15. Figure P1 shows scatter plots of revenues and expenses for the Federal Employees Health Benefits (FEHB) program for fiscal years 1984 to 1996, both in billions of dollars.
    1. In which years did FEHB make a profit?
    2. In which years did FEHB lose money?
    3. What was FEHB's best financial year during the period shown?
    Figure P1  Federal Employees Health Benefits Program Financial Data
    Source: US Office of Personnel Management 1998 Fact Book

16. 1. Use the information in Figure P1 to make a table of profits for FEHB from 1984 to 1996. (Treat a loss as a negative profit.)
    2. Use your table to make a scatter plot of profits for FEHB.
    3. Find the total profit (or loss) for FEHB over the entire period shown.