Question

9. If I have a sample of 200 randomly selected people in a city of whom 120 are Christians, what would be a 95% confidence interval for the proportion of Christians in that city? If I want my confidence interval with a margin of error of 1% or less, how many people should I have in my sample?

please show in excel in with formulas

Answer 1

The sample proportion is computed as:

The 95% confidence interval is obtained as:

=

=

= (0.532,0.668)

Using excel function 'CONFIDENCE',

With n = 200, std. dev. =

=

= 0.0679

Hence, the confidence interval is given by

To estimate the sample size:

= 9219.84 = 9220

To obtain the confidence interval with a margin of error of 1% or less, we would need to sample an estimated no. of 9220 people.