A randomly chosen sample of NYC college students were asked

A randomly chosen sample of NYC college students were asked if they take public transportation to get to classes. 175 out of 200 people in the sample indicated that they do take public transportation. Construct a 95% confidence interval for the true proportion of NYC college students who take public transportation to get to classes.

Solution

P = 175 / 200 = 0.875

Q = 1 - 0.875 = 0.125

n = 200

alpha = 1 - 0.95 =0.05

alpha / 2 = 0.025

Z= 1.96 [ from tables of Z distribution]

we are using Z distribution because this problem is about proportion, when you have problmes of proportion you always use Z distribution

I : 0.875 +/- 1.96 * srqt [ (0.875*125) / 200 ]

I : 0.875 +/- 0.0458

I: 0.8292 , 0.9208