Question

Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years. a. Calculate a 95% two-sided confidence interval on the death rate from lung cancer. b. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03

Answer 1

a. The 95% confidence interval is 0.799<p<0.847

b. The sample size n is 622

Explanation:

A

P^ = 823/1000

= 0.823

At 95% confidence interval

P^ +- z-alpha/2√p^(1-p^)/n

z-alpha/2 = 1.96

When we insert values we get:

0.823+-1.96√0.823(1-0.823)/1000

= 0.823+-1.96√0.000145671

= 0.823+-1.96(0.012069)

= (0.8467, 0.7993)

The 95% confidence interval is 0.799<p<0.847

B.

We are to compute the sample size here.

The formula and full calculation has been done in the attachment.

4268.4x0.145671

= 621.78

= 622

n = 622