Question

6. A recent Gallop poll showed Trump's approval rating 40% with a margin or error of 3%.

a) Find the confidence interval,
c) Does the confidence interval support that more than 50% of Americans approve of
Trump? Why or why not?

Answer 1

Explained below.

Explanation:

The (1 - α)% confidence interval for the population proportion is:

`CI=\hat p\pm MOE`

Given:

`\hat p=0.40\\MOE=0.03`

(a)

Compute the confidence interval as follows:

`CI=\hat p\pm MOE`

`=0.40\pm0.03\\\\=(0.37, 0.43)`

(b)

Since the confidence interval consists of values less than 50%, it implies that there is not enough evidence to suggest that more than 50% of Americans approve of Trump.