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).

Question

Mathematics

Freddy Ware

30 April, 17:46

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).

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Adelyn Rangel · 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%.

Step-by-step 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%.