Question

A research group conducted an extensive survey of 3170 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?" 1520 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,

n = 3170

x = 1520

Point estimate = sample proportion = = x / n = 1520 / 3170=0.479

1 - = 1 - 0.479=0.521

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

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

= 1.645 (((0.479*0.521) / 3170)

= 0.015

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.479 - 0.015 < p < 0.479 + 0.015

0.464< p < 0.494

The 90% confidence interval for the population proportion p is : lower limit =0.464 upper limit=0.494