Question

A random sample of 225 items from a population results in 60% possessing a given characteristic. Using this information, the researcher constructs a 99% confidence interval to estimate the population proportion. The resulting confidence interval is _______.

Answer 1

Solution :

Given that,

n = 225

=60% = 0.60

1 - = 1 - 0.60= 0.40

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 * (((0.60 * 0.40) / 225) = 0.0841

A 99 % confidence interval for population proportion p is ,

- E < P < + E

0.60 - 0.0841 < p < 0.60 +0.0841

0.5159 < p <0.6841

The 99% confidence interval for the population proportion p is : ( 0.5159 , 0.6841)