If an author was to conduct a survey, how many adults must be surveyed in order

Question

If an author was to conduct a survey, how many adults must be surveyed in order to be 95% confident that the sample percentage is in error by no more than three percentage points?
A) assume that a recent poll showed that 80% of adults make online purchases. B) assume that we have no prior information suggesting a possible value of the population proportion. If an author was to conduct a survey, how many adults must be surveyed in order to be 95% confident that the sample percentage is in error by no more than three percentage points?
A) assume that a recent poll showed that 80% of adults make online purchases. B) assume that we have no prior information suggesting a possible value of the population proportion.
A) assume that a recent poll showed that 80% of adults make online purchases. B) assume that we have no prior information suggesting a possible value of the population proportion.

Explanation / Answer

a) n = z^2 * pq/e^2

here p = 0.8 , q = 0.2 , e = 0.03

for 95 % , z = 1.96

n = 1.96^2 * 0.8 *0.2 / 0.03^2

= 682.9511

minimum sample size = 683

b) if   we have no prior information

n = z^2 /(4 e^2)

= 1.96^2 / (4 * 0.03^2 )

= 1067.111

hence minimum sample size = 1068

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