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Math Help - Confidence intervals

  1. #1
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    Confidence intervals

    The test was developed in the 1980s for screening donated blood for the presence of
    HIV. The test is designed to detect antibodies, substances produced in the body of donors car-
    rying the virus; however, the test is not 100% accurate. The developer of the test claimed that
    the test would produce fewer than 5% false positives and fewer than 1% false negatives. In
    order to evaluate the accuracy of the test, 1,000 persons known to have HIV and10,000 per-
    sons known to not have HIV were given the test. The following results were tabulated:

    True State of Patient
    Test Result Has HIV Does Not Have HIV Total
    Positive Test 993 591 1,584
    Negative Test 7 9,409 9,416
    Total 1,000 10,000 11,000

    a. Place a 95% confidence interval on the proportion of false positives produced by the test.
    b. Is there substantial evidence (alpha=.05 ) that the test produces less than 5% false
    positives?



    upper question continued:


    Place a 95% confidence interval on the proportion of false negatives produced by
    thetest.
    b. Is there substantial evidence ( ) that the test produces less than 1% false
    negatives?
    c. Which of the two types of errors, false positives or false negatives, do you think is
    more crucial to public safety? Explain your reasoning.
    (Ott. An Introduction to Statistical Methods and Data Analysis, 6th Edition. Brooks/Cole/CourseSmart, 12/30/2008. 547).
    <vbk:PBK70000LTI00535#page(547)>
    Last edited by mr fantastic; October 13th 2009 at 02:24 AM. Reason: Merged posts
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  2. #2
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    I found a, remaining b

    what is Is there substantial evidence ( .05) that the test produces less than 5% false positives?

    do i just answer it directly, or am i to put hypothesis testing H0: p>=.05 versus Ha: p<.05?
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