Question

A research group conducted an extensive survey of 2933 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?" 1499 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 ___

Answer 1

Here total wage and salaried workers = 2933

Here total responded positive = 1499

sample proportion = p^ = 1499/2933 = 0.511

confidence interval = 90%

crtiical test statistic = 1.645

margin of error (MOE) = critical test statsitic * standard error of mean

standard error of mean = sqrt [p^ * (1-p^)/n] = sqrt [0.511 * (1 - 0.511)/2933]

= 0.015

90% confidence interval = p^ +- MOE = 0.511 +- 0.015

Lower Limit = 0.511- 0.015 = 0.496

Upper Limit = 0.511 + 0.015 = 0.526