a telephone

your lab notebook

Objective: To estimate what fraction of toll-free numbers are already in use, and how close the U.S. is to adding a new toll-free prefix to 1-800, 1-877, and 1-888.

1. At home, compose a set of seven-digit numbers to call. Generate these using the letters on the telephone dial. Examples (using 1-800 as a generic toll-free prefix):

1-800-DAVESAD, 1-800-MYDISCO, 1-800-CLINTON, 1-800-EATBEET, 1-800-4ASHARK, 1-800-SATANRX, 1-800-VINEGAR, etc.

**No credit will be given for obscene or offensive texts.**

2. You will need at least ten seven-character texts.

**No credit will be given for texts replicated by another student, so be creative!**

3. Call each number. Use each toll-free prefix: this means you will make at least thirty calls. (I.e., for the example above, you will call 1-800-DAVESAD, 1-877-DAVESAD, and 1-888-DAVESAD, for three separate calls from that text.) Use the digit 7 for Q and 9 for Z.

4. Record the response in your lab notebooks (person picked up, voice mail picked up, answering machine picked up, nobody picked up, number-not-in-service recording, busy signal). Also, where applicable, record the name of the persons or businesses who hold the number. If you reach a live human being, you may ask them if they are aware that their phone number spells out a text (if you do so, record their answer), though you are not required to do so.

5. Submit the numbers you called, and the responses you received, to me. I will then: A) compile the numbers into a spreadsheet, with responses. B) Credit will be withdrawn for obscene or duplicated numbers. C) Confirm a random sample of the numbers by calling them myself from home; your grade for the assignment will be set at zero if I am unable to confirm more than three of your phone calls. D) Grades for the first stage of the project will be compiled and assigned. E) The spreadsheet will be distributed to the class for statistical analysis.

6. Answer the following questions in your lab report: A) How many toll-free numbers are possible, given three prefixes followed by seven digits? B) What percentage of toll-free telephone numbers are already assigned? C) What percentage is corporate? Personal? Governmental? Are these percentages more or less than you expected? D) If another prefix were to be added, would it be more likely to serve business and corporate interests than private individuals? E) In what ways were the numbers we selected to call not a random sampling of all possible telephone numbers? (

*Hint: What digits were used preferentially, or avoided?*)

*Some answers are located in comments.*

## 2 comments:

Answer for question A):

Each digit in the seven end digits may be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. Thus there are ten possibilities for each of these, and three possibilities for prefixes. The number of possible toll-free numbers is now:

3*(10)(10)(10)(10)(10)(10)(10) = 30,000,000

For question E):

The selection is non-randomly biased against the digits 1 and 0, because neither of them are associated with letters on the telephone keypad. It is also biased against digits which are associated with uncommon letters (as for example 5, which is matched with J, K, and L, two of which are very uncommon), and toward digits associated with common ones (for example, 7, which is matched with P, Q, R, and S).

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