A research group conducted an extensive survey of 3002 wage and salaried workers

Question

A research group conducted an extensive survey of 3002 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sample. In response to the question, "What does success mean to you?" 1486 responded, "Personal satisfaction from doing a good job." Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question. How large a sample is needed if we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 1.2% of the population percentage? (Hint: Use p 0.50 as a preliminary estimate. Round your answer up to the nearest whole number.)

Explanation / Answer

At 95% Confidence interval the critical value is z0.025 = 1.96

Margin of error = 0.012

Or, z0.025 * sqt(P * (1 - P)/n) = 0.012

Or, 1.96 * sqrt(0.5 * 0.5/n) = 0.012

Or, sqrt(n) = 1.96 * sqrt(0.5 * 0.5)/0.012

Or, sqrt (n) = 81.67

Or, n = 6670

= 0.5 +/-;

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