# Can someone please check my working out - 2nd year stat/probability question

• laura_a
In summary: actually have the disease will get a false negative, not "5% of the negatives will be false". 5% of 18= 2.7 out of 1000 or 0.5% will have a false negative as in the caculation above.
laura_a

## Homework Statement

I will write the question on about below will write my answers, I would appreciate anyone letting me know if I'm right/wrong. Thanks
Q. A test for a disease has a false negative rate of 5%, false positive rate of 15%. The prevalance of the disease is 1.8%
b) if the popluation were screened, what proportion will test negative to disease
c) what proportion of those testing negative will actually HAVE the disease
d) explain why this proportion is so small

## The Attempt at a Solution

b) P(not disease) U P(false neg)

P(Disease) = 18/1000
P(not disease) = 982/1000
p(false neg) = 5/100

P (not D) U (false neg) = 982/1000 + 5/100 - (982/1000 * 5/100)
= 9829/10,000

This means 9829/10000 or 98.29% will test negative
c) how many of these actually have the disease... well I assume it is just 5% of that number because the given details say 5% test false neg.. so 5% * 98.29 = 4.91%

d) the proportion is 5% of just under 100 so that is why it is lower than the given 5% ?? not sure about d)

laura_a said:

## Homework Statement

I will write the question on about below will write my answers, I would appreciate anyone letting me know if I'm right/wrong. Thanks
Q. A test for a disease has a false negative rate of 5%, false positive rate of 15%. The prevalance of the disease is 1.8%
b) if the popluation were screened, what proportion will test negative to disease
c) what proportion of those testing negative will actually HAVE the disease
d) explain why this proportion is so small

## The Attempt at a Solution

b) P(not disease) U P(false neg)

P(Disease) = 18/1000
P(not disease) = 982/1000
p(false neg) = 5/100

P (not D) U (false neg) = 982/1000 + 5/100 - (982/1000 * 5/100)
= 9829/10,000

This means 9829/10000 or 98.29% will test negative
I don't understand why you did that calculation. In a population of 1000 people (to avoid the fractions), 18 will have the disease and 982 will not. Of the 982 who do not, 5%= .05(982()= 49.1 will have a false negative. Of the 18 who have the disease, 15%= .15(18)= 2.7 will have a false positive so the other 15.3 will report negative. There will be a total of 49.1+ 15.3= 64.4 negatives out of 1000 or 6.44%

c) how many of these actually have the disease... well I assume it is just 5% of that number because the given details say 5% test false neg.. so 5% * 98.29 = 4.91%
5% of the people who actually have the disease will get a false negative, not "5% of the negatives will be false". 5% of 18= 2.7 out of 1000 or 0.5% will have a false negative as in the caculation above.

[/quote]d) the proportion is 5% of just under 100 so that is why it is lower than the given 5% ?? not sure about d)[/QUOTE]
It is so small, because the number of people who actually have the disease is very small compared with the number who do not. The number of false positives is much larger than the number of false negatives because it is based on a larger population.

laura_a said:

## Homework Statement

I will write the question on about below will write my answers, I would appreciate anyone letting me know if I'm right/wrong. Thanks
Q. A test for a disease has a false negative rate of 5%, false positive rate of 15%. The prevalance of the disease is 1.8%
b) if the popluation were screened, what proportion will test negative to disease
c) what proportion of those testing negative will actually HAVE the disease
d) explain why this proportion is so small

## The Attempt at a Solution

b) P(not disease) U P(false neg)

P(Disease) = 18/1000
P(not disease) = 982/1000
p(false neg) = 5/100

P (not D) U (false neg) = 982/1000 + 5/100 - (982/1000 * 5/100)
= 9829/10,000

This means 9829/10000 or 98.29% will test negative
I don't understand why you did that calculation. In a population of 1000 people (to avoid the fractions), 18 will have the disease and 982 will not. Of the 982 who do not, 5%= .05(982()= 49.1 will have a false positive and the other 932.9 will test negative. Of the 18 who have the disease, 15%= .15(18)= 2.7 will have a false negative. There will be a total of 932.9+ 2.7= 936.6 negatives out of 1000 or 93.66%

c) how many of these actually have the disease... well I assume it is just 5% of that number because the given details say 5% test false neg.. so 5% * 98.29 = 4.91%
5% of the people who actually have the disease will get a false negative, not "5% of the negatives will be false". 5% of 18= 2.7 out of 1000 or 0.5% will have a false negative as in the caculation above.

[/quote]d) the proportion is 5% of just under 100 so that is why it is lower than the given 5% ?? not sure about d)[/QUOTE]
It is so small, because the number of people who actually have the disease is very small compared with the number who do not. The number of true negatives is much larger than the number of false negatives because it is based on a larger population.

## 1. What is the purpose of checking my working out for a 2nd year stat/probability question?

The purpose of checking your working out is to ensure that you have correctly solved the problem and have applied the appropriate statistical and probability concepts. This helps to avoid any mistakes and ensures that you have a clear understanding of the problem.

## 2. How do I know if my working out is correct?

You can check your working out by comparing it to the answer provided or by using a calculator or statistical software to verify your calculations. Additionally, you can ask a classmate or a teacher to review your working out and provide feedback.

## 3. Is it necessary to show my working out for a 2nd year stat/probability question?

Yes, it is important to show your working out for a 2nd year stat/probability question as it demonstrates your understanding of the concepts and allows for easier identification of any mistakes. It also helps others to follow your thought process and provide feedback if needed.

## 4. How much detail should I include in my working out?

You should include enough detail in your working out to show your calculations and reasoning behind each step. This may include writing out formulas, showing substitutions, and providing clear explanations for your choices. However, avoid including unnecessary steps or information.

## 5. Can I use a different method than the one taught in class for my working out?

It is recommended to use the method taught in class for your working out, as it is likely the most appropriate and efficient approach for the problem. However, if you choose to use a different method, make sure to clearly explain your reasoning and show how it leads to the correct answer.

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