Math Stats Help?

Question

In a Gallop poll of 567 randomly selected adults, 274 said they were underpaid. Construct a 95% confidence interval estimate for the percentage of all adults who said they were underpaid.

Answer 1

Hello, thank you for taking the time to post your question!

The underlying formula that you want to use when doing confidence intervals for proportions is to take

p-hat +/- z* (sqrt(p-hat(1 – p-hat))/n))

for this set of information we have

p-hat = 274/567 = 0.4832

z* = 1.96 for a confidence level of 95%

n = 567

so putting it all together gives

0.4832 +/- 1.96(sqrt(0.4832(1 – 0.4832)/567

=0.4832 +/- 0.04116

=0.4420 to 0.5244

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

274/567 =np = mean percentage who say they are underpaid

it's a binominal distribution, two outcomes, under or not under paid

p=274/567, q=1-p=(567-274)/567 = 293/567

Variance = npq = 567(274/567)(293/567) = 274(293)/567

standard deviation = sqrVar

use the binomial to estimate a normal distribution