A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.05 with 99% confidence if
(a) she uses a previous estimate of 0.36?
(b) she does not use any prior estimates?
The ESTIMATED SAMPLE PROPORTION should be calculated using the following formula: n = p̂q̂
(a)
Now, with a PRELIMINARY ESTIMATE of .36, p̂ = .36, and q̂ = 1 - p̂ = 1 - .36 = .64
Since this is a 99% CONFIDENCE INTERVAL, then significance level is , and so,
E (Margin of Error) = .05
Therefore, n = p̂q̂ becomes:
(b)
Now, since NO PRELIMINARY ESTIMATE WAS GIVEN/WAS AVAILABLE, then .5(50%) should be used for p̂, or for the ASSUMED proportion
With p̂ being .5, q̂ = 1 - p̂ = 1 - .5 = .5
Since this is a 99% CONFIDENCE INTERVAL, then significance level is , and so,
E (Margin of Error) = .05
Therefore, n = p̂q̂ becomes:
When I used STATDISK to calculate the ESTIMATED SAMPLE PROPORTION, I got the same result: a) 612 and b) 664 adults.
This problem looks a lot like one from Chamberlain College of Nursing. I tutor a lot of nursing students who attend that college. Is that where you attend?