if based on a sample size of 850 a political candidate finde

if based on a sample size of 850, a political candidate finde that 458 people would vote for him in a two person race, what is the 95% confidence interval for his expected proportion of the vote? would he be confident of winning based on this poll? use the appropriate formula and verify your result using the confidence intervals workbook

Solution

p = 458 / 850 = 0.54

q = 1 - 0.54 = 0.46

n = 850

alpha = 1-0.95=0.05

alpha/2 = 0.025

Z = 1.96 [ from tables of normal distribuiton]

I: 0.54 +/- 1.96 * srqt [ (0.54*0.46) / 850 ]

0.54 +/- 0.0335

0.5065 < p < 0.5735

would he be confident of winning based on this poll?

yes because the proportion in the confidence interval is up to 0.50 = 50%