Question

If n = 400 and ˆpp^ (p-hat) = 0.25, construct a 95% confidence interval.

Give your answers to three decimals

Answer 1

Solution :

Given that,

n = 400

Point estimate = sample proportion = = x / n = 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) / 400)

E = 0.042

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.25 -0.042< p < 0.25+0.042

0.208< p < 0.292