SOLUTION: 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 0.0

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Question 1060911: 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?

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
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?

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