Question

2. A random sample of 121 observations produced a sample proportion of 0.25. An approximate 95% confidence interval for the population proportion p is between

Answer 1

Solution :

Given that,

n = 121

Point estimate = sample proportion = = 0.25

1 -   = 1- 0.25 =0.75

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 (((0.25*0.75) /121 )

E = 0.0772

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.25-0.0772 < p <0.25+ 0.0772

0.1728< p < 0.3272

The 95% confidence interval for the population proportion p is : 0.1728, 0.3272