Question

Medical tests for diagnosing conditions such as being positive for COVID19 are not perfect, just like decisions in hypothesis tests. In such tests, the null hypothesis is that the person does not have the condition being tested for. Answer the following questions about the table below.

		Test Result
		Do Not Reject H0 Test for COVID19 is Negative	Reject H0 Test for COVID19 is Positive
Truth	H0 TRUE Person does Not Have COVID19	A	B
	HA TRUE / H0 FALSE Person has COVID19	C	D

1. Write a sentence to describe the outcome in Box A. Does this outcome mean that an error was made? If so, explain what kind of error: Type 1 or Type 2?

2. Write a sentence to describe the outcome in Box B. Does this outcome mean that an error was made? If so, explain what kind of error: Type 1 or Type 2?

3. Write a sentence to describe the outcome in Box C. Does this outcome mean that an error was made? If so, explain what kind of error: Type 1 or Type 2?

4. Write a sentence to describe the outcome in Box D. Does this outcome mean that an error was made? If so, explain what kind of error: Type 1 or Type 2?

Answer 1

As the table is not in the correct alignment i am assuming it is as follows:

	Test for covid 19 is negative	Test for covid 19 is positive
Person do not have covid 19	A	B
Person has covid 19	C	D

Explanation for A

The outcome of box A is the person do not have covid 19 and the test reports are negative.

No this does not make any kind of error because given that Ho is true we aren't rejecting Ho through the test.

Explanation for B

The outcome for box B is the that test shows that the person is having covid 19 but in fact he does not have covid 19.

Yes this is a kind of error because we are rejecting Ho given that it is true, this kind of error is termed as type 1 error.

Explanation for C

the outcome for box C is that the tests show that the person does not have covid 19 but in fact he does have covid 19.

Yes, this is a kind of error because we are not rejecting the false null hypothesis, this kind of error is termed as type 2 error.

Explanation for D

The outcome for box D is such that the tests shows the person has covid 19 and the person in fact really has covid 19.

This is not an error because we are rejecting the null hypothesis given that it is false.