Two Way Table2018-10-25T14:50:20+10:00

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  • AdminAdmin

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    Post count: 573

    gen_prob_0002
    A test for tuberculosis was conducted on 100 people. The results are shown in the table.
    a. Describe what a false positive result is.
    b. How many people had a false positive result?
    c. What percentage of these people had accurate result?
    d. What percentage of the people who had a negative test result actually had the disease?

    a. A false positive is when the test result incorrectly indicates you have the disease, when you don’t

    b. A false positive would be the not accurate people without the disease: 6

    c. accurate result = 92 out of 100
    92/100 × 100
    = 92%

    d. The people who had a negative test result include the people with the disease who had a not accurate (2) and the people without the disease who had an accurate (88).
    Out of these 90 people, only 2 actually had the disease: 2/90 × 100 = 2.2%

  • AdminAdmin

    Keymaster
    Post count: 573

    The two-table below shows the results of a new lie detector which is used by NSW police in conjunction with random breathe testing.

     
    Detector Results
    Told the Truth
    Lied
    Total
    Accurate Result
    Inaccurate Result
    154
    96
    21
    12
     
    250
    33
    Total
     175
     108
    283

    What percentage of people who did tell the truth were told they lied?

    The people who told the truth would be those that were told they told the truth and had an accurate result = 154
    Those who were told they lied and had an inaccurate result = 12
    total who told the truth = 166

    The percentage that were told they lied would be = $$\frac{12}{166}\times 100$$
    = 7.2%

  • AdminAdmin

    Keymaster
    Post count: 573

    A new test has been developed for determining whether or not people are carriers of the Gaussian virus. A two way table was used to record the results.

     
    Test Results
    Positive
    Negative
    Total
    Carrier
    Not Carrier
    74
    14
    16
    96
     
    88
    112
    Total
    90
    110
     

    a. How many people were tested?
    b. A person selected from the group is not a carrier of the virus. What is the probability that the test results would show this?
    c. For how many of the people tested were their test results accurate?
    a. total = 88 + 112
    = 200

    b. there are 112 people that are not carriers, out of those 96 have a negative result – ie showing they are not a carrier
    P = $$\frac{96}{112}$$

    = $$\frac67$$

    c.  an accurate result would mean:
    carrier receiving a positive result = 74
    non carrier receiving a negative result = 96
    accurate = 74 + 96
    = 170

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