Q1) Confidence Intervals: Company wishes to conduct telephone survey of randomly selected voters to evaluate proportion of voters who favour a particular candidate in presidential election, to within 2% error with 95% confidence.  It is guessed that proportion is 53%.

i) Determine the required minimum sample size?

ii) Project manager assigned to survey is not sure about actual proportion or about 2% error limit. Proportion may be anywhere from 40% to 60%. Create a table for minimum sample size required with half-width ranging from 1% to 3% and actual proportion ranging from 40% to 60%.

ii) Inspect table produced in question 2 above. Comment on relative sensitivity of minimum sample size to actual proportion and to desired half width.

iii) At what value of actual proportion is required sample size maximum?

iv) Cost of polling includes fixed cost of $425 and variable cost of $1.20 per person sampled, therefore cost of sampling n voters is $(425 + 1.20n). Tabulate cost for range of values as in question 2 above.

v) A competitor of company which had announced results to within +/- 3% with 95% confidence has started to announce results to within +/- 2% with 95% confidence.  Project manager wishes to go one better by improving company's estimate to be within +/- 1% with 95% confidence. What would you tell manager?