A research group conducted an extensive survey of 3071 wage and salaried workers

Question

A research group conducted an extensive survey of 3071 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?" 1515 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. Find a 90% confidence interval for p. (Round your answers to three decimal places.) lower limit upper limit

Explanation / Answer

p is given as 1515/3071=0.4933

z for 90% confidence is 1.65

thus the lower bound is p-z*Sqrt(p*(1-p)/N)=0.4933-1.65*sqrt(0.4933*(1-0.4933)/3071)=0.478

upper bound is p+z*Sqrt(p*(1-p)/N)=0.4933+1.65*sqrt(0.4933*(1-0.4933)/3071)=0.508

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