Question 1205357
p = 112/300
q = 1 - p = 1 - 112/300 = 300 /300 - 112/300 = (300 - 112)/300 = 188/300.
standard error = sqrt(112/300 * 188/300 / 300) = .027926.
98% two tail confidence interval requires a z-score of plus or minus 2.326.
z = (x-m)/s
z = plus or minus 2.326.
x = x
m = p = 112/300 = .373333
s = .027963.
on the low end of the confidence interval, -2.326 = (x-.373333)/.027963.
solve for x to get x = -2.326 * .027963 + .373333 = .30829.
on the high end of the confidence interval, 2.326 = (x - .373333)/.027963.
solve for x to get x = 3.236 * .027963 + .373333 = .43837.
your 98% confidence interval is from .30829 to .43837.


this is what it looks like using z-scores.


<img src = "http://theo.x10hosting.com/2023/121221.jpg">


this is what it looks like using raw scores.


<img src = "http://theo.x10hosting.com/2023/121222.jpg">


in the z-score formula:
z = the z-score
x = the sample proportion
m = the mean proportion which is equal to p
s = the standard error.


p is equal to the proportion of the sample size that favor an NDP candidate.
q = 1-p is equal to the proportion of the sample size that do not favor an NDP candidate.
the mean proportion is equal to p which is equal to m in the z-score formula.