Question

A research group conducted an extensive survey of 2944 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?" 1600 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

Solution :

Given that,

Point estimate = sample proportion = = x / n = 1600 / 2944 = 0.543

1 - = 1 - 0.543 = 0.457

Z/2 = 1.645

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 * (((0.543 * 0.457) / 2944)

Margin of error = E = 0.015

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.543 - 0.015 < p < 0.543 + 0.015

0.528 < p < 0.558

lower limit: 0.528

upper limit: 0.558