Question

Suppose that we have a test for a rare disease, and the test is 95 percent accurate. Given a population of 10000 people, of whom 2 percent have the disease, answer the following questions. You may give exact answers, or decimals rounded to three decimal places. How many people have the disease? How many people who have the disease test positive for the disease? How many people do not have the disease? How many people who do not have the disease test positive for the disease? If someone tests positive for the disease, what is the probability that they actually have the disease? If someone tests negative for the disease, what is the probability that they actually do not have the disease?

          Suppose that we have a test for a rare disease, and the test is 95 percent accurate. Given a population of 10000 people, of whom 2 percent have the disease, answer the following questions. You may give exact answers, or decimals rounded to three decimal places.
How many people have the disease?
How many people who have the disease test positive for the disease?
How many people do not have the disease?
How many people who do not have the disease test positive for the disease?
If someone tests positive for the disease, what is the probability that they actually have the disease?
If someone tests negative for the disease, what is the probability that they actually do not have the disease?

Show more…

Suppose that we have a test for a rare disease, and the test is 95 percent accurate. Given a population of 10000 people, of whom 2 percent have the disease, answer the following questions. You may give exact answers, or decimals rounded to three decimal places.
How many people have the disease?
How many people who have the disease test positive for the disease?
How many people do not have the disease?
How many people who do not have the disease test positive for the disease?
If someone tests positive for the disease, what is the probability that they actually have the disease?
If someone tests negative for the disease, what is the probability that they actually do not have the disease?

Added by Samuel A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Joanna Quigley

03/31/2023

Step 1

How many people have the disease? Out of 10000 people, 2 percent have the disease. So, the number of people with the disease is: 0.02 x 10000 = 200 Show more…

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Suppose that we have a test for a rare disease, and the test is 95 percent accurate. Given a population of 10000 people, of whom 2 percent have the disease, answer the following questions. You may give exact answers, or decimals rounded to three decimal places. How many people have the disease? How many people who have the disease test positive for the disease? How many people do not have the disease? How many people who do not have the disease test positive for the disease? If someone tests positive for the disease, what is the probability that they actually have the disease? If someone tests negative for the disease, what is the probability that they actually do not have the disease?

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Transcript

00:01 We've been given some information, and i'm going to turn that into probability notation.

00:06 So there's a test for a rare disease, and we know that 2 % of the population have the disease.

00:12 So probability of somebody having the disease, we'll just put d, is 2%.

00:18 So the test is 95 % accurate.

00:22 So the probability of testing positive, given that you have the disease, will be 95%.

00:26 The probability of testing positive given you don't have the disease will be only 5%.

00:35 So that's what it's meaning by accuracy.

00:39 So basically the probability of giving the correct result, whether you have the disease or not.

00:45 Now let's have a look at some questions.

00:48 Part a, how many people have the disease? well, 2 % of 10 ,000.

00:52 So we'll take our proportion, 1 .02, and we'll supply it by 10 ,000.

00:58 Of course this won't work if you do 2 times 10 ,000.

01:01 But let's see what we get.

01:05 So that's 200 people.

01:10 How many who have the disease will test positive? so there's 200 people.

01:15 Out of that, 95 % will test positive.

01:22 So 0 .95.

01:26 So that is 190 of them.

01:31 The over 10 will test negative.

01:33 How many people don't have the disease? well, you either have the disease or you either have the disease.

01:37 Don't.

01:38 If 200 people have it, 9 ,800 do not...

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