Question

3. Of 1000 randomly selected cases of lung cancer, 450 resulted in death within 5 years. Calculate a 96% CI on the death rate from lung cancer.

Answer 1

The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).

Explanation:

In a sample with a number n of people surveyed with a probability of a success of
`\pi`, and a confidence level of
`1-\alpha`, we have the following confidence interval of proportions.

`\pi \pm z\sqrt{(\pi(1-\pi))/(n)}`

In which

z is the z-score that has a p-value of
`1 - (\alpha)/(2)`.

Of 1000 randomly selected cases of lung cancer, 450 resulted in death within 5 years.

This means that
`n = 1000, \pi = (450)/(1000) = 0.45`

96% confidence level

So
`\alpha = 0.04`, z is the value of Z that has a p-value of
`1 - (0.04)/(2) = 0.98`, so
`Z = 2.054`.

The lower limit of this interval is:

`\pi - z\sqrt{(\pi(1-\pi))/(n)} = 0.45 - 2.054\sqrt{(0.45*0.55)/(1000)} = 0.4177`

The upper limit of this interval is:

`\pi + z\sqrt{(\pi(1-\pi))/(n)} = 0.45 + 2.054\sqrt{(0.45*0.55)/(1000)} = 0.4823`

The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).