A company wants to conduct a telephone survey of randomly selected voters who favor a particular candidate in a presidential election, to within 2% error with 95% confidence. It is guessed that the population is 53%.

1. What is the minimum sample size?

2. The project manager assigned to the survey is not sure about the actual portion size or the 2% error limit. The proportion may be anywhere from, 40% to 60%. Construct a table for the minimum sample size required with half-width ranging from 1% to 3% and the actual proportion ranging from 40% to 60%.

Table 1: Minimum sample size required for a 95% confidence

3. Inspect the table produced in question 2 above. Comment on the relative sensitivity of the minimum sample size to the actual proportion and to the desired half-width.
Form table 1, it can be seen that for a fixed proportion (p), as the desired half-width (E) decreases, the minimum sample size required increases very rapidly. Further, for a desired half-width, the minimum sample size is maximum for a proportion of 50%. The reason for this is that the maximum value of is 0.25.

4. At what value of the actual proportion is the actual sample size the maximum?

The actual sample size is the maximum at 50% of the actual proportion.

5. The cost of polling includes a fixed cost of \$425 and a variable cost of \$1.20 per person sampled, thus the cost of sampling n voters is \$(425 + 1.20n). Tabulate the cost for range of values as in question 2 above.

Table 2: Cost for range of minimum sample size for a 95% confidence

6. A competitor of the company that had announced results to within +/-3% with 95% confidence has started to announce results within +/-2% with 95% confidence. The project manager wants to go one better by improving the company’s estimate within +/-1% with 95% confidence. What would you tell the manager?

The cost of sampling voters within +/-1% with 95% confidence is very high (about 4 times) as compared to within +/-2% with 95% confidence. Therefore, I would tell the project manager not to go one better by improving the company’s estimate within +/-1% with 95% confidence. It will only incur an increase cost without any considerable benefit.