Question

In a random sample of 144 observations, = .7. The 95% confidence interval for p is

Answer 1

Solution :

Given that,

n = 144

Point estimate = sample proportion = = 0.7

1 -   = 1-0.7 =0.3

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 (((0.7*0.3) /144 )

E = 0.075

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.7 - 0.075 < p < 0.7+0.075

0.625< p < 0.775