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Given confidence level of 95% and sample size n=97, number of successes x=46. Find a...

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surfer3 | Valedictorian

Posted June 3, 2012 at 4:03 PM via web

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Given confidence level of 95% and sample size n=97, number of successes x=46. Find a confidence interval for the population proportion p.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted June 3, 2012 at 4:38 PM (Answer #1)

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You need to use the central limit theorem to determine the confidence interval for population proportion p such that:

`(hatp - 1.96sqrt(hatp(1-hatp)/n) ,hatp+ 1.96sqrt(hatp(1-hatp)/n)) `

You need to evaluate `hatp`  such that:

`hatp = 46/97 = 0.474`

`1 - hatp = 1 - 0.474 = 0.526`

`hatp(1 - hatp )/n = 0.0025 =gt sqrt (hatp(1 - hatp )/n) = 0.050`

`1.96*sqrt (hatp(1 - hatp )/n) = 0.098`

`hatp - 1.96*sqrt (hatp(1 - hatp )/n) = 0.474 - 0.098 = 0.376`

`hatp+ 1.96*sqrt (hatp(1 - hatp )/n) = 0.474 - 0.098 = 0.572`

Hence, evaluating the confidence interval for the population proportion p yields `(0.376 , 0.572).`

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