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 canc

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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.

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Bơ 3 years 2021-07-23T09:44:28+00:00 1 Answers 43 views 0

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  1. Cherry
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    2021-07-23T09:46:17+00:00
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    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).

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