Question

Assume that a sample is used to estimate a population proportion p. Find the 95% confidence interval for a sample of size 287 with 207 successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.

< p

Answer 1

Solution :

Given that,

n = 287

x = 207

Point estimate = sample proportion = = x / n = 207/287=0.721

1 -   = 1- 0.721 =0.279

At 95% confidence level the z is ,

= 1 - 95% = 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 (((0.721*0.279) / 287)

= 0.052

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.721-0.052 < p <0.721+ 0.052

0.669< p < 0.773