By failing to prepare, you are preparing to fail.
Two Way Table2021-01-01T11:18:14+10:00

Timetable › Forums › Standard › Probability & Relative Frequency › Two Way Table

Tagged: , ,

Viewing 5 posts - 1 through 5 (of 5 total)
  • Author
    Posts
  • Admin
    Keymaster
    October 29, 2016 at 10:45 am
    Post count: 1622
    #9733
    Two-Way Tables

    •    A positive result means that the test has indicated you have the disease.
    •    A negative result means that the test indicated that you do not have the disease.
    •    A false positive result means that you have been told you have the disease when you do not.
    •    A false negative result means you have been told you do not have the disease when you actually do have it.
    •    An accurate positive result means that you have been told you have the disease when you actually do have it.
    •    An accurate negative result means that you have been told you do not have the disease when you really don’t have it.

    It is VERY important that you read the table carefully, understanding what each cell means. A slight change in the setup can change the interpretation dramatically.

    Admin
    Keymaster
    November 29, 2018 at 3:01 pm
    Post count: 1622
    #14866

    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%

    Admin
    Keymaster
    November 29, 2018 at 3:02 pm
    Post count: 1622
    #14869

    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%

    Admin
    Keymaster
    January 1, 2021 at 11:19 am
    Post count: 1622
    #18886

    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

    Admin
    Keymaster
    January 1, 2021 at 11:19 am
    Post count: 1622
    #18887
      Test Results
      Accurate Not Accurate Total
    With Disease 130 70 200
    Without Disease 250 50 300
    Total 380 120 500

    130 = Accurate positive: The number of people who were accurately told they do have the disease. ie, told they have it and do have it
    70 = False negative: The number of people who were falsely told they do not have the disease. ie, told they do not have it and do have it
    200 = The total number of people with the disease

    250 = Accurate negative: The number of people who were accurately told that they do not have the disease. ie, told they do no have it and do not have it
    50 = False positive: The number of people who were falsely told they have the disease. ie, told they have it and do not have it
    300 = The total number of people without the disease

    380 = Total number of accurate results
    120 = Total number of false/inaccurate results
    500 = Total number

    Here is another table, set up slightly differently.

      Test Results
      Test Positive Test Negative Total
    With Disease 130 70 200
    Without Disease 250 50 300
    Total 380 120 500

    130 = Positive result + disease. So this would be an accurate positive. ie, told they have it and do have it
    70 = Negative + disease. So this would be a false negative. ie, told they do not have it and do have it
    200 = The total number of people with the disease

    250 = Positive + no disease. So this would be a false positive. ie, told they have it and do not have it
    50 = Negative + no disease. So this would be an accurate negative. ie, told they do no have it and do not have it
    300 = The total number of people without the disease

    380 = Total number of positive results
    120 = Total number of negative results

  • Author
    Posts
Viewing 5 posts - 1 through 5 (of 5 total)
  • You must be logged in to reply to this topic.

maths made easy

copyright © 1995 – 2025

Privacy Policy

ABN: 86 396 190 036

Show Buttons
Hide Buttons
Go to Top