Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    Name:  Screen Shot 2013-04-05 at 1.08.33 AM.png
Views: 76
Size:  62.7 KB
    Name:  Stats Question003.jpg
Views: 96
Size:  363.8 KB

    I've attached the question and my current working out thus-far. I'm stuck with part D.
    Offline

    13
    ReputationRep:
    (Original post by BananaPie)
    Name:  Screen Shot 2013-04-05 at 1.08.33 AM.png
Views: 76
Size:  62.7 KB
    Name:  Stats Question003.jpg
Views: 96
Size:  363.8 KB

    I've attached the question and my current working out thus-far. I'm stuck with part D.
    Find the value for the critical region of the 5% significance level for the \chi^{2} probability density function and compare that to \chi^{2}_{calc}.

    If \chi^{2}_{calc} < \chi^{2} then you accept the null hypothesis
    • Thread Starter
    Offline

    0
    ReputationRep:
    I understand that my degree of freedom of 1, so does that mean that

    (2/9)(x-45)^2 < x^2pdf(0.05,1)
    ?
    Offline

    13
    ReputationRep:
    (Original post by BananaPie)
    I understand that my degree of freedom of 1, so does that mean that

    (2/9)(x-45)^2 < x^2pdf(0.05,1)
    ?
    If x^2pdf(0.05, 1) represents the critical value at the 5% significance level for 1 degree of freedom, then yes
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Felix Felicis)
    If x^2pdf(0.05, 1) represents the critical value at the 5% significance level for 1 degree of freedom, then yes
    as x^2(0.05,1) = 1.74 (3sf)

    Doing that I get 42.2<x<47.8 which turns into x = 43,44,45,46,47

    However the answer includes 41,42,48,49 as well. I'm missing something =S
    Offline

    13
    ReputationRep:
    (Original post by BananaPie)
    as x^2(0.05,1) = 1.74 (3sf)

    Doing that I get 42.2<x<47.8 which turns into x = 43,44,45,46,47

    However the answer includes 41,42,48,49 as well. I'm missing something =S
    I got \chi^{2} = 3.841 which made my range of x values 40.84 &lt; x &lt; 49.15 thus x = 41, 42, 43, 44, 45, 46, 47, 48, 49
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Felix Felicis)
    I got \chi^{2} = 3.841 which made my range of x values 40.84 &lt; x &lt; 49.15 thus x = 41, 42, 43, 44, 45, 46, 47, 48, 49
    Where did you get 3.841 from? =[

    Edit: It's written in the data booklet /facepalm. But surely there's a way to calculate it via GDC?
    Offline

    13
    ReputationRep:
    (Original post by BananaPie)
    Where did you get 3.841 from? =[
    http://whichbobareyou.com/uploads/2/...5_orig.png?288

    I used a different statistics table which gave it to 3 decimal places but 3.84/ 3.841 same thing :P
    Offline

    13
    ReputationRep:
    (Original post by BananaPie)
    Where did you get 3.841 from? =[

    Edit: It's written in the data booklet /facepalm. But surely there's a way to calculate it via GDC?
    I usually use the stats table to work out the critical values and don't have a GDC, sorry :P
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Felix Felicis)
    http://whichbobareyou.com/uploads/2/...5_orig.png?288

    I used a different statistics table which gave it to 3 decimal places but 3.84/ 3.841 same thing :P
    Yeah, the data booklet we have for our exam includes all the critical values for x^2 distribution. I was pretty sure there was a way to calculate it via GDC though so I was occupied on finding out how. =S

    Thanks for the help! ^^
    Offline

    13
    ReputationRep:
    (Original post by BananaPie)
    Yeah, the data booklet we have for our exam includes all the critical values for x^2 distribution. I was pretty sure there was a way to calculate it via GDC though so I was occupied on finding out how. =S

    Thanks for the help! ^^
    GDCs are for wimps bro

    No problem! Best of luck with your IB exams! I do A-levels but go to a school which does IB as well
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Felix Felicis)
    GDCs are for wimps bro

    No problem! Best of luck with your IB exams! I do A-levels but go to a school which does IB as well
    Wimps!? XD They reduce the time taken to solve questions on my stat paper by like 70%-80%.

    And thanks =]. Good luck on ur A-Level exams if you're taking them this year as well!
    Offline

    13
    ReputationRep:
    (Original post by BananaPie)
    Wimps!? XD They reduce the time taken to solve questions on my stat paper by like 70%-80%.

    And thanks =]. Good luck on ur A-Level exams if you're taking them this year as well!
    I just had an idea...does your graphics calculator have an equation solver?
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Felix Felicis)
    I just had an idea...does your graphics calculator have an equation solver?
    Equation Solver? It may have one, but I probably don't know it's called an "Equation Solver". I use a Ti84 Plus.
    Offline

    13
    ReputationRep:
    (Original post by BananaPie)
    Equation Solver? It may have one, but I probably don't know it's called an "Equation Solver". I use a Ti84 Plus.
    It should do...

    But I was thinking, if you let \chi^{2} (t) denote the probability density function for the \chi^{2} function.

    Then by definition P(X \leq p) = \displaystyle\int_{0}^{x} \chi^{2} (t) dt

    If your graphics calculator had an equation solver, then you could solve \displaystyle\int_{x}^{\infty} \chi^{2} (t) dt = 0.05 for x and you should get the critical value Alternatively, use the data booklet
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Felix Felicis)
    It should do...

    But I was thinking, if you let \chi^{2} (t) denote the probability density function for the \chi^{2} function.

    Then by definition P(X \leq x) = \displaystyle\int_{-\infty}^{x} \chi^{2} (t) dt

    If your graphics calculator had an equation solver, then you could solve \displaystyle\int_{x}^{\infty} \chi^{2} (t) dt = 0.05 for x and you should get the critical value Alternatively, use the data booklet
    Perhaps it does, I'll have to ask my teacher if such a thing exists on our version of the GDC. I've never heard of it done that way before so it's surprising, but I'll have to check and see.

    The thing about the data booklet is that I keep forgetting we have a table of values. It's a habit of mine to believe that everything can be given to u on a GDC if it's a calc paper, unless the question itself is algebraic.
    Offline

    13
    ReputationRep:
    (Original post by BananaPie)
    Perhaps it does, I'll have to ask my teacher if such a thing exists on our version of the GDC. I've never heard of it done that way before so it's surprising, but I'll have to check and see.

    The thing about the data booklet is that I keep forgetting we have a table of values. It's a habit of mine to believe that everything can be given to u on a GDC if it's a calc paper, unless the question itself is algebraic.
    I found this which might be of interest :]

    http://www.dummies.com/how-to/conten...on-solver.html

    Edit: Not saying you're a dummy! :P
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Felix Felicis)
    I found this which might be of interest :]

    http://www.dummies.com/how-to/conten...on-solver.html

    Edit: Not saying you're a dummy! :P
    Wait. Is Equation Solver an "Application"? Or is it a program that is hidden somewhere? Because if it's an application then the only ones I'm allowed are 1)Finance, 2) CtlgHelp and 3) PlySmlt2
    Offline

    13
    ReputationRep:
    (Original post by BananaPie)
    Wait. Is Equation Solver an "Application"? Or is it a program that is hidden somewhere? Because if it's an application then the only ones I'm allowed are 1)Finance, 2) CtlgHelp and 3) PlySmlt2
    No idea :dontknow:
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Would you like to hibernate through the winter months?
    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

    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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