Question

Statistics Question (Confidence Intervals)

It was found that x people in a sample of 225 supported a smoking ban in public places. If the 95% confidence interval for the proportion of people supporting the ban in the population from which the sample was taken is [0.2297,0.3481] calculate the value of x.

Answer 1

\[\frac{x}{225}-1.96\frac{\sigma}{\sqrt{225}}=0.2297\ ........(1)\]
\[\frac{x}{225}+1.96\frac{\sigma}{\sqrt{225}}=0.3481\ ........(2)\]
Adding equations (1) and (2) gives
\[\frac{2x}{225}=0.5778\ .............(3)\]
Now you just need to solve equation (3) to find the value of x

Answer 2

Oh, ok thanks! I did it similarly but wasn't sure it was the correct answer because they are giving you "an interval where x could be 95% of the time" so you can't be absolutely certain what x is....

Answer 3

The interval is where the population mean will occur in repeated samples 95% of the time. x is a specific number of people in a particular sample.