A company 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% confidence1. It is guessed that the proportion is 53%.
(a) What is the required minimum sample size?
(b) The project manager assigned to the survey is not sure about the actual proportion or about the 2% error limit. Construct a table for the minimum sample size required with margin of error ranging from 1% to 3% and actual proportion ranging from 40% to 60%.
(c) Inspect the table produced in question (b) above. Comment on the relative sensitivity of the minimum sample size to the actual proportion and to the desired margin of error.
(d) At what value of the actual proportion is the required sample size the maximum?
(e) 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 the range of values in question (b) above.
(f) 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?
1 The 2% error is in absolute value, i.e., the 95% C.I. for the estimated proportion should be proportion±2%.
Attachment:- Assignment.rar