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

Answer:

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

Step-by-step 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.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$.

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

This means that $n = 1000, \pi = \frac{450}{1000} = 0.45$

96% confidence level

So $\alpha = 0.04$, z is the value of Z that has a p-value of $1 - \frac{0.04}{2} = 0.98$, so $Z = 2.054$.  

The lower limit of this interval is:

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

The upper limit of this interval is:

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

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