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, 252 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 = 252

a) Point estimate = sample proportion = = x / n = 252 / 1000 = 0.2520

1 - = 1 - 0.2520 = 0.7480

b) At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.96 (((0.2520 * 0.7480) / 1000)

= 0.027

A 95% confidence interval for population proportion p is ,

± E   

= 0.2520  ± 0.027

= ( 0.225, 0.279 )

lower limit = 0.225

upper limit = 0.279

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

= 1.96 (((0.2520 * 0.7480) / 1000)

= 0.027