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# Sample size problem set

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% 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 + or - 3% with 95% confidence has started to announce results to within + or - 2% with 95% confidence. The project manager wants to go one better by improving the company's estimate to be within + or - 1% with 95% confidence. What would you tell the manager?

#### Solution Preview

This is a set of solutions to six problems all related to finding the ...

#### Solution Summary

This is a set of solutions to six problems all related to finding the minimum sample size necessary to estimate a population parameter with a given maximum allowable error and a given level of confidence.

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