Question

Calculate a 99% confidence interval for population proportion when the population proportion is 0.826 and n=92. Thank you!

Answer 1

Solution :

Given that,

n = 92

Point estimate = sample proportion = =0.826

1 - = 1 - 0.826=0.174

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 (((0.826*0.174) / 92)

= 0.1018

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.826 -0.1018 < p < 0.826 +0.1018

0.7242< p < 0.9278

The 99% confidence interval for the population proportion p is : (0.7242 , 0.9278)