Question

use the normal distrubution. A 95 percent confidence interval for p given that p=0.36 and n=475. find the best point estimate margin of error and the 95 percent confidence interval is __ to __.

Answer 1

Solution :  

Given that,

n = 475

Point estimate = sample proportion = = 0.36

1 - = 1 - 0.36 = 0.64

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 * (((0.36 * 0.64) / 475)

= 0.043

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.36 - 0.043 < p < 0.36 + 0.043

0.317 < p < 0.403

The 95 percent confidence interval is 0.317 to 0.403