Question

A random sample of 121 observations produced a sample proportion of 0.4. An approximate 95% confidence interval for the population proportion p is between

Answer 1

Solution :

Given that,

n = 121

Point estimate = sample proportion = = 0.4

1 - = 1 - 0.4 = 0.6

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.4 * 0.6) / 121)

= 0.087

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.4 - 0.087 < p < 0.4 + 0.087

0.313 < p < 0.487

(0.313 , 0.487)

n approximate 95% confidence interval for the population proportion p is between 0.313 ans 0.487 .