Question

A certain survey conducted had a population proportion of at most 22% for people who agreed. What is the confidence level if 20% of the people sampled agreed, and the standard error of the proportion is ±1%?

Answer 1

@perl

Answer 2

The sample proportion is given as 20% , and we are told at most the population proportion is 22% . That tells us that the confidence interval is 20% ±2%.
We are also given that the standard error, the standard deviation of the sample proportions, is 1%. Therefore 22% is 2 standard deviations above 20%.
By the empirical rule, 95% of the data are within 2 standard deviations of a normally distributed variable.

Answer 3

The wording of the question is a bit strange to me, though.

Answer 4

I know! Ive been trying to understand this question for an hour I don't like the wording

Answer 5

the margin of error is 2% , since it can go from 20% up to 22%

Answer 6

Let's plug this into a formula.
$$ \Large {
\rm Margin~ of~ error = Z_c \cdot standard ~error
\\~\\
2\% = Z_c \cdot 1\%

}
$$

So Z_c must equal to 2. what is the confidence level for z score of 2?

Answer 7

I'll look it up rn