Question

A random sample of 300 random people from a geographic area indicated that 50 of 

them had received vaccine. Estimate the true proportion of people who had been vaccinated with 95% confidence.

Answer 1

Solution:

$\hat p=\frac{50}{300}=\frac16$

$n=300$

$\hat q=1-\frac16=\frac56$

For 95% confidence interval, $z=1.96$

Now, 95% confidence interval$=(\hat p\pm z\sqrt{\frac{\hat p \hat q}{n}})$

$=(\frac16\pm 1.96\sqrt{\frac{\frac16. \frac56}{300}}) \\=(0.1244,0.2088)$