Question

Chinovac Labs tried a new vaccine on 126 randomly selected individuals. From the experiment, it was determined that 118 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 point estimate of this interval?

Answer 1

In this case, p = 118/126 =0.94

We compute the confidence interval using the formula:

$CI=p \plusmn z\sqrt{\frac{p(1-p)}{n}}$

where p = sample proportion

n = sample size

z = critical value

From the standard normal table, the critical value for 95% confidence interval z= ±1.96 (for two-tailed test)

Therefore, the 95% confidence interval is:

$95 \% CI=0.94+1.96\sqrt{\frac{0.94(1-0.06)}{126}}=0 94 \plusmn 0.04$

The lower limit = 0.94-0.04 = 0.9

The upper limit = 0.94+0.04 = 0.98

Answer: The 95% confidence interval is (0.90, 0.98)