In: Statistics and Probability
A research group conducted an extensive survey of 2875 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?" 1519 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.)
upper limit =
lower limit =
n = 2875
x = 1519
Point estimate = sample proportion = = x / n = 1519 / 2875 = 0.528
1 - = 1 - 0.528 = 0.472
At 90% confidence level the z is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
Z/2 = Z0.05 = 1.645
Margin of error = E = Z / 2 * √ (( * (1 - )) / n)
= 1.645 * (√((0.528 * 0.472) / 2875)
= 0.015
A 90% confidence interval for population proportion p is ,
- E < p < + E
0.528 - 0.015 < p < 0.528 + 0.015
0.513 < p < 0.543
The 90% confidence interval for the population proportion p is : 0.513 , 0.543
upper limit = 0.513
lower limit =0.543