Question

If i know that my confidence interval is 0.32<p<0.42 for Californians that are Religious and i know that alpha is equal to 0.01 to solve for the interval... what would i know about the confidence interval?

Answer 1

We have alpha = 0.01 which means the given confidence interval is 99% confidence interval of proportion.

The 99% CI of p is 0.32<p<0.42

From the given CI of p we can know many information which are listed below:

We can get the margin of error from above CI as below:

Hence the sample estimate of p can be obtained as below:

We also know that the formula for margin of error is

We have α=0.01, zα/2 = z0.005 = 2.575829

So,

Hence the sample size, i.e. n= 619

Interpretation of 99%CI of p:

We can be 99% confident that proportion of Californians that are Religious is between 0.32 and 0.42