Question

. In an exit poll, for which the sample size is 2797, the sampling distribution of the sample proportion voting for the incumbent has mean 0.554 and standard deviation 0.009. Find an interval of values within which the sample proportion will almost certainly fall. P.S please, write legibly!!! thanks

Answer 1

Solution:

We are given

n = 2797

We are given mean for sampling distribution for proportion = 0.554

So, we have estimate for p = 0.554

We are given standard deviation for sampling distribution for proportion = 0.009

We know that the estimate for the standard deviation for the sampling distribution of proportion is equal to the standard error.

So, we have estimate for standard error = 0.009

We assume 99% confidence level.

Critical Z value = 2.5758

(by using z-table)

Margin of error = Z*Standard error

Margin of error = E = 2.5758*0.009

Margin of error = E = 0.023182

Lower limit = p – E = 0.554 - 0.023182 = 0.530818

Upper limit = p + E = 0.554 + 0.023182 = 0.577182

Confidence interval = (0.531, 0.577)