please show work Problem 17 Blood tests are used to screen p

please show work

Problem 17. Blood tests are used to screen possible donors for HIV. You perform the following test Null Hypothesis: Donor does not have HIV. Alternative Hypothesis: Donor has HIV. The test indicated that the donor does not have HTV even though the donor does have HIV. What type of error is this? Justify your answer.

This is a case of failing to reject false null hypothesis, and is called type II error.