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
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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) (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
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