Question

A simple random sample of 600 individuals provides 100 Yes responses.

a. What is the point estimate of the proportion of the population that would provide Yes responses (to 2 decimals)?

Later use p(average) rounded to 2 decimal places.

b. What is your estimate of the standard error of the proportion (to 4 decimals)?

c. Compute the 95% confidence interval for the population proportion (to 4 decimals).

Answer 1

Solution :

Given that,

n = 600

x = 100

a)

Point estimate = sample proportion = = x / n = 0.17

1 - = 0.83

b)

Standard error of the proportion,

= (p*(1-p))/n =  (0.17*0.83)/600 = 0.0153

c)

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

Margin of error = E = Z / 2 *

= 1.96 * 0.0153

= 0.0301

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.17 - 0.0301 < p < 0.17 + 0.0301

0.1399 < p < 0.2001

( 0.1399 , 0.2001 )