Turn on thread page Beta
    • Thread Starter
    Offline

    17
    ReputationRep:
    Hi guys i have a quick question about q11 part c. If the probability of success changes by calculating it from the data, then the expected values will change.

    So the test statistic will change as well as the critical value as the degree of freedom changes.

    So do we assume that the change in expected values and thus the test statistic are negligible so that we can reach the answer in part c in solution bank?




    Thanks
    Posted on the TSR App. Download from Apple or Google Play
    • Very Important Poster
    Offline

    21
    ReputationRep:
    Very Important Poster
    (Original post by Shaanv)
    Hi guys i have a quick question about q11 part c. If the probability of success changes by calculating it from the data, then the expected values will change.

    So the test statistic will change as well as the critical value as the degree of freedom changes.

    So do we assume that the change in expected values and thus the test statistic are negligible so that we can reach the answer in part c in solution bank?




    Thanks
    Blows my mind for sure.

    The only thing I can think of is that you would expect the estimate to be fairly close to 0.5 (analogous to throwing say 100 times a fair coin, you might get 47 heads and hence estimate a probability of 0.47, not far off 0.5), hence expected values similar hence ...

    Seems like a stinker of a question.
    Offline

    14
    ReputationRep:
    (Original post by Shaanv)
    Hi guys i have a quick question about q11 part c. If the probability of success changes by calculating it from the data, then the expected values will change.

    So the test statistic will change as well as the critical value as the degree of freedom changes.

    So do we assume that the change in expected values and thus the test statistic are negligible so that we can reach the answer in part c in solution bank?

    Thanks
    You are quite right. If you plow through the calculations, you get a value for the binomial parameter of 0.486875, and a value of \chi^2 of 4.4778, and therefore the conclusion of the question stands.

    There is a sneaky way to answer the question fully, though, without re-doing the calculations this way. You know that the value of \chi^2 must be less for the estimated binomial parameter (can you see why?) and therefore the conclusion stands if the previous version of \chi^2 is less than the new critical value.

    The answer given in the solutions bank is inadequate.
    • Thread Starter
    Offline

    17
    ReputationRep:
    (Original post by Gregorius)
    You are quite right. If you plow through the calculations, you get a value for the binomial parameter of 0.486875, and a value of \chi^2 of 4.4778, and therefore the conclusion of the question stands.

    There is a sneaky way to answer the question fully, though, without re-doing the calculations this way. You know that the value of \chi^2 must be less for the estimated binomial parameter (can you see why?) and therefore the conclusion stands if the previous version of \chi^2 is less than the new critical value.

    The answer given in the solutions bank is inadequate.
    Because binomial parameter is calculated from the data the expected values are closer to the observed so the \chi^2 value decreases and must be less than the old \chi^2 value.

    As old \chi^2 value is less than new critical value, then new \chi^2 value must also be less than new critical value.

    Is that correct?

    Thanks for the help.
    Posted on the TSR App. Download from Apple or Google Play
    Offline

    14
    ReputationRep:
    (Original post by Shaanv)
    Because binomial parameter is calculated from the data the expected values are closer to the observed so the \chi^2 value decreases and must be less than the old \chi^2 value.
    Yes, that's it, though I realized after posting that this is trickier to justify than I thought!

    As old \chi^2 value is less than new critical value, then new \chi^2 value must also be less than new critical value.

    Is that correct?
    Yes.
 
 
 

University open days

  • Heriot-Watt University
    School of Textiles and Design Undergraduate
    Fri, 16 Nov '18
  • University of Roehampton
    All departments Undergraduate
    Sat, 17 Nov '18
  • Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 17 Nov '18
Poll
Black Friday: Yay or Nay?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.