Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a survey of 1000 large corporations, 244 said that, given a choice between a job candidate who smokes and an equally qualified nonsmoker, the nonsmoker would get the job.

(a) Let p represent the proportion of all corporations preferring a nonsmoking candidate. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 0.95 confidence interval for p. (Round your answers to three decimal places.)

lower limit
upper limit

What is the margin of error based on a 95% confidence interval? (Round your answer to three decimal places.)

Answer 1

Solution :

Given that,

n = 1000

x = 244

Point estimate = sample proportion = = x / n = 244/1000=0.2440

1 -   = 1- 0.2440 =0.7560

At 0.95 confidence level the z is ,

= 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.2440*0.7560) / 1000)

= 0.027

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.2440-0.027 < p <0.2440+ 0.027

0.217< p < 0.271

The 95% confidence interval for the population proportion p is : lower limit=0.217,upper limit= 0.271