Question

In a survey of 3937 adults, 706 say that they have seen a ghost. Construct a​ 99% confidence interval for the population proportion. Interpret the results.

In a survey of 2311 adults, 727 say they believe in UFOs. Find the 99% confidence interval for the population proportion of adults who believe in UFOs.

Answer 1

We know that population proportion confidence interval is given by:

where based on the sample

A)

So based on the sample of ghost CI is given by:

and

is the critical value at level of significance.

Which we have calculated in R

So 99% Confidence interval is given by:

(0.1635759, 0.1950729)

Interpretation :

It can be interpreted from the CI that if we randomly draw 100 sample from the population then on an average 99 samples will have proportion between the above given range (0.1635759, 0.1635759)

B)

Similarly proportion of people believe in UFO

we can find the 99% CI

here

x = 727

n = 2311

( 0.2892783, 0.3390211)