The test for screening donated blood for the presence of the AIDS virus is designed to detect antibodies; however is not 100% accurate. It is claimed that the test would produce fewer than 5% false positives and fewer than 1% false negatives. To evaluate accuracy 1,000 people with AIDs and 10,000 people without AIDs were given the test.

Test result Has AIDs Doesnt have AIDs Total

Positive test 993 591 1584

Negative test 7 9409 9416

Total 1000 10000 11000

1- Place 99% confidence interval on the proportion of false positives produced by the test

2- Is the substantial evidence (alpha= 0.01) that the test produces less than 5% false positives

3- Place 99% confidence interval on the proportion of false negatives produced by the test

4- Is the test substantial evidence ( alpha=0.01) that the test produces less than 2% false negatives

5- Which of the two types of error, false positives or false negatives, do you think is more crucial to public safety. Explain.