Question

A random sample of adults in the United States were asked whether football was their favorite sport. The resulting confidence interval for the proportion of U.S. adults who answered "yes" is (0.58,0.72). What is the sample proportion, p^?

Answer 1

The sample proportion is p=0.65.

Explanation:

We have a confidence interval for the propotion of U.S. adults who answered "yes" when they were asked whether football was their favorite sport.

This confidence interval is symmetric around the sample proportion, so we can calculate it as the average of the upper and lower bound.

We can also get there from the way the bounds (UL and LL) are calculated:

`LL=p-MOE\\\\UL=p+MOE`

MOE: margin of error

Then,

`UL+LL=(p+MOE)+(p-MOE)=2p\\\\\\p=(UL+LL)/(2)`

In this case UL=0.72 and LL=0.85, so p is calculated as:

`p=(UL+LL)/(2)=(0.72+0.58)/(2)=(1.30)/(2)=0.65`