Question

Explain the meaning of a poll that says 44% of Americans approve of the president's policies, with a margin of error of 2% and confidence level of 90%. In % of such polls, the reported approval of the president's policies will be between % (smaller value) and % (larger value).

Answer 1

We are 90% sure that the true proportion of Americans who approve the ppresident's policies is in the interval from 42% to 46%.

Explanation:

A confidence interval of a proportion p% at the x% level with m% margin of error means that:

We are x% sure that the true mean of the population is in the interval from (p-x)% to (p+x)%.

In this problem, we have that

90% confidence level

44% with a margin of error of 2%

So:

We are 90% sure that the true proportion of Americans who approve the ppresident's policies is in the interval from 42% to 46%.