Question

Alice wants to estimate the percentage of people who plan on voting yes for the upcoming school levy. She surveys 380 individuals and finds that 260 plan on voting yes. What is the correct interpretation of the confidence interval

Answer 1

Step-by-step explanation:

Sample proportion $\hat{p} = 260/380 = 0.684$

90% confidence interval for p is

$\hat{p} - Z\times \sqrt(\hat{p}( 1 - \hat{p}) / n) < p < \hat{p} + Z\times \sqrt(\hat{p}( 1 - \hat{p}) / n)$

$0.684 - 1.645\times \sqrt ( 1 -0.684) / 380) < P < 0.684 + 1.645\times \sqrt ( 1 -0.684) / 380)$

0.645 < p < 0.723

Interpretation - We estimate with 90% confidence that the true population proportion of people who plan  on voting yes on the levy between 0.645 and 0.723.