SOLUTION: Out of 300 people sampled, 177 preferred Candidate A. Based on this, estimate what proportion of the voting population (p) prefers Candidate A. Use a 90% confidence level, and g

Algebra ->  Statistics  -> Confidence-intervals -> SOLUTION: Out of 300 people sampled, 177 preferred Candidate A. Based on this, estimate what proportion of the voting population (p) prefers Candidate A. Use a 90% confidence level, and g      Log On


   

Question 1187550: Out of 300 people sampled, 177 preferred Candidate A. Based on this, estimate what proportion of the voting population (p) prefers Candidate A.
Use a 90% confidence level, and give your answers as decimals, to three places.
_______ < P > ________
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
p = 177 / 300 = .59
q = 1 - p = .41

mean proportion = p = .59

standard error = sqrt(p * (1-p / 300) = sqrt(.59 * .41 / 300) = .028396.

critical z-score at 90% confidence level is plus or minus 1.645.

use the z-score formula to find the critical raw score.

for the low side, z = (x - m) / s becomes:

-1.645 = (x - .59) / .028396.
solve for x to get:

x = -1.645 * .0283960091 + .59 = .54329.

for the high side, z = (x - m) / s becomes:

1.645 = (x - .59) / .028396.

solve for x to get:

x = 1.645 * .028396. + .59 = .63671.

at 90% confidence level, your proportion will be between .54329 and .63671, when you have a mean of .59 and a standard error of .028396.

here's what it looks like on a z-score normal distribution calculator output.



the calculator i used can be found at https://davidmlane.com/hyperstat/z_table.html