Question

Assume that population proportion is to be estimated from the sample described. Use the sample results to approximate the margin of error and​ 95% confidence interval.

Sample​ size: n = 560. p-hat = 0.8

(560*0.8 = 448 = # of successes)

Find the​ 95% confidence interval.

Answer 1

Solution :

Given that,

n = 560

Point estimate = sample proportion = = 0.8

1 -   = 1- 0.8 =0.2

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 (((0.8*0.2) / 560)

E = 0.0331

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.8-0.0331 < p < 0.8+0.0331

0.7669< p < 0.8331

The 95% confidence interval for the population proportion p is : 0.7669,0.8331