Question

A research group conducted an extensive survey of 2941 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?" 1606 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 = 1606 / 2941 = 0.546

1 - = 1 - 0.546 = 0.454

Z/2 = Z0.05 = 1.645

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

= 1.645 (((0.546 * 0.454) / 2941)

= 0.015

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.546 - 0.015 < p < 0.546 + 0.015

(0.531 < p < 0.561)

lower limit = 0.531

upper limit = 0.561