Answer to Question #307399 in Statistics and Probability for secret

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 ± 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± 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)

The point estimate = (upper limit + Lower limit)/2

= (0.98 + 0.90)/2

= 0.94

Answer: 0.94