document.write( "Question 1062598: A researcher wants to estimate with 99% confidence, the proportion of people who have a computer desktop. A previous study showed that 30% of those interviewed had a computer desktop at home. The researcher wants to be accurate within 3% of the true proportion. What is the minimum sample size to be needed? \n" ); document.write( "
Algebra.Com's Answer #677594 by MathTherapy(10552)\"\" \"About 
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A researcher wants to estimate with 99% confidence, the proportion of people who have a computer desktop. A previous study showed that 30% of those interviewed had a computer desktop at home. The researcher wants to be accurate within 3% of the true proportion. What is the minimum sample size to be needed?
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See Probability-and-statistics/1060911 below. \r\n" );
document.write( "Do it the same way. You only need a) though.\r\n" );
document.write( "Pay attention to the different values. For example, in yours, Margin of Error (E) is: 3% (.03) instead of 5% (.05).\r\n" );
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document.write( "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\r\n" );
document.write( "​(a) she uses a previous estimate of 0.36​?\r\n" );
document.write( "​(b) she does not use any prior​ estimates?\r\n" );
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document.write( "The ESTIMATED SAMPLE PROPORTION should be calculated using the following formula: n = p̂q̂\"matrix%281%2C2%2C+%22%2A%22%2C+%28Z%5Bc%5D%2FE%29%5E2%29\"\r\n" );
document.write( "(a)\r\n" );
document.write( "Now, with a PRELIMINARY ESTIMATE of .36, p̂ = .36, and q̂ = 1 - p̂ = 1 - .36 = .64\r\n" );
document.write( "Since this is a 99% CONFIDENCE INTERVAL, then significance level is \"matrix%281%2C3%2C+.01%2F2%2C+or%2C+.005%29\", and so, \"Z%5Bcritical%5D+=+2.575\"\r\n" );
document.write( "E (Margin of Error) = .05\r\n" );
document.write( "Therefore, n = p̂q̂\"matrix%281%2C2%2C+%22%2A%22%2C+%28Z%5Bc%5D%2FE%29%5E2%29\" becomes: 
(b)\r\n" );
document.write( "Now, since NO PRELIMINARY ESTIMATE WAS GIVEN/WAS AVAILABLE, then .5(50%) should be used for p̂, or for the ASSUMED proportion\r\n" );
document.write( "With p̂ being .5, q̂ = 1 - p̂ = 1 - .5 = .5\r\n" );
document.write( "Since this is a 99% CONFIDENCE INTERVAL, then significance level is \"matrix%281%2C3%2C+.01%2F2%2C+or%2C+.005%29\", and so, \"Z%5Bcritical%5D+=+2.575\"\r\n" );
document.write( "E (Margin of Error) = .05\r\n" );
document.write( "Therefore, n = p̂q̂\"matrix%281%2C2%2C+%22%2A%22%2C+%28Z%5Bc%5D%2FE%29%5E2%29\" becomes: \r\n" );
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document.write( "When I used STATDISK to calculate the ESTIMATED SAMPLE PROPORTION, I got the same result: a) 612 and b) 664 adults.
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document.write( "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? \n" );
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