Question

	H0 is True	Ha is True
	Test result is negative: Patient not diagnosed with HIV	Test result is positive: Patient diagnosed with HIV
Reject H0	Type 1 Error (example 1)	Correct (example 2)
Patient does have HIV	Test result is negative & inaccurate	Test result is positive and accurate
Fail to Reject H0	Correct (example 3)	Type 2 Error (example 4)
Patient does not have HIV	Test result is negative and accurate	Test result is positive & inaccurate

Please explain what the table above mean in hypothesis Ho, Ha

Answer 1

The given table explains the Type I error and Type II error. We know that the type I error is defined as the probability of rejecting the null hypothesis H₀ when it is true. The type II error is defined as the probability of do not rejecting the null hypothesis H₀ when it is not true. For the given scenario of testing hypothesis, the null and alternative hypotheses are given as below:

Null hypothesis: H₀: Patient is not diagnosed with HIV.

Alternative hypothesis: H_a: Patient is diagnosed with HIV.

The type I error for the above scenario is defined as the probability of rejecting the null hypothesis that patient is not diagnosed with HIV, however actually patient don’t have HIV.

The type II error for the above scenario is defined as the probability of do not rejecting the null hypothesis that patient is not diagnosed with HIV, however actually patient have HIV.

When we reject the null hypothesis H₀ and conclude that alternative hypothesis H_a is true, and then there is no existence of any type of error. In this case, decision is correct.

When we do not reject the null hypothesis H₀ and conclude that the null hypothesis H₀ is true, then there is no existence of any type of error. In this case, decision is correct.