Question

Chinovac Labs tried a new vaccine on 312 randomly selected individuals. From the experiment, it was determined that 128 of them developed immunity. Calculate a 95% confidence interval for the proportion p of individuals in the population for whom the vaccine would help. What is the upper bound of this interval?

Answer 1

Because you want a 95% confidence interval, your z-value is 1.96.

From a sample of 312 individuals were found 128 individuals with developed immunity. So

$\hat{p} = \frac{128}{312} =0.41$

The formula for a confidence interval for a population proportion is

$\hat{p}±z \times \sqrt{\frac{\hat{p}(1- \hat{p})}{n}}$

Find

$\hat{p}\frac{1 - \hat{p}}{n} = 0.41 \frac{1-0.41}{312} = 0.000775$

Take the square root to get 0.0278

Multiply your answer by z.

This step gives you the margin of error.

$1.96 \times 0.0278 = 0.0544$

Confidence interval:

0.41±0.0544

The upper bound of this interval = 0.41+0.054 = 0.464