Question

Use the normal distribution to find a confidence interval for a proportion P given the relevant sample results. Give the best point estimate for P, the margin of error, and the confidence interval. Assume the results come from a random sample.

A 99% confidence interval for p given that p = 0.36 and n= 550

Point estimate =

Margins of error =

The 99% confidence interval is _______ to _______

Answer 1

Solution :

Given that,

= 0.36

1 - = 1 - 0.36 = 0.64

n = 550

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * (((0.360 * 0.640) / 550)

= 0.053

A 99 % confidence interval for population proportion p is ,

- E < P < + E

0.360 - 0.053 < p < 0.360 + 0.053

0.307 < p < 0.413

The 99% confidence interval for the population proportion p is : ( 0.307 , 0.413)