Question

Question: In survey 4001 adults 718 say they see a ghost construct 99% confidence interval for the proportion.

A 99% confidence interval for the population proportion is (), () round three decimal places. Interpret the results

Answer 1

Solution :

Given that,

n = 4001

x = 718

= x / n = 718 / 4001= 0.179

1 - = 1 - 0.179= 0.821

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 * (((0.179 * 0.821) / 4001) = 0.0156

A 99 % confidence interval for population proportion p is ,

- E < P < + E

0.179 - 0.0156< p < 0.179 + 0.0156

0.1634 < p < 0.1946

The 99% confidence interval for the population proportion p is fall between lower bound and upper bound  ( 0.1634 , 0.1946)