Acompany wants to conduct a telephone survey of randomly selected voters to estimate the proportion of voters who favor a particular candidate in a presidential election, to within 2% error with 95% confidence. It is guessed that the proportion is 53%.
1. What is the required minimum sample size?
2. The project manager assigned to the survey is not sure about the actual proportion or about 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 actual proportion ranging from 40% to 60%.
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.
4. At what value of the actual proportion is the required sample size the maximum?
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.
6. A competitor of the company that had announced results to within 3% with 95% confidence has started to announce results to within 2% with 95% confidence. The project manager wants to go one better by improving the company’s estimate to be within 1% with 95% confidence. What would you tell the manager?