Confidence Intervals and Critical Values

Announcements Posted on
Four things that unis think matter more than league tables 08-12-2016
    • Thread Starter
    Offline

    0
    ReputationRep:
    Right, I understand that a confidence interval is calculated from:

    Mean +/- Critical value * Standard error

    What I don't understand is how you calculate the critical value for a given confidence interval. I realise that for a 95% confidence interval the critical value is +/- 1.96 but I don't understand how this is calculated or how to calculate it for other percentages. Can anyone help me?

    (I've tried looking through the formula booklet but I can't see the critical values tabulated anywhere)
    Offline

    1
    ReputationRep:
    For a random variable Z, with normal distribution, mean=0 and variance=1

    P(Z<1.96)=0.975
    P(Z<-1.96)=0.025
    P(-1.96<Z<1.96)=0.95

    You can get these values from a table which you should have been given.
    • Thread Starter
    Offline

    0
    ReputationRep:
    I *think* I've found the table you're referring to. Is it Page 24 of this:

    http://www.aqa.org.uk/qual/pdf/FORMULAE.PDF ?

    If it is, I don't suppose you could give me an idea of how to use it:o: , for example how I'd find the critical values for a 60% confidence interval?
    Offline

    1
    ReputationRep:
    (Original post by windsock)
    I *think* I've found the table you're referring to. Is it Page 24 of this:

    http://www.aqa.org.uk/qual/pdf/FORMULAE.PDF ?

    If it is, I don't suppose you could give me an idea of how to use it:o: , for example how I'd find the critical values for a 60% confidence interval?
    Yes, that's the one.

    For 60% you can think of three regions...lowest 20% middle 60% and top 20%.

    80% are below the top 20% so you need to look up a probability of 0.8 in the body of the table.

    You should get a value of about 0.84.
    • Thread Starter
    Offline

    0
    ReputationRep:
    I understand what you're saying about the regions and how you get to 0.8

    I'm still a bit stumped about using the table itself though. I've found the value closest to 0.8 (0.80234) in the body of the table but I'm not sure how to convert this into an actual value - which side of the table should I be reading off? Sorry if this sounds dumb:o:
    Offline

    1
    ReputationRep:
    (Original post by windsock)
    I understand what you're saying about the regions and how you get to 0.8

    I'm still a bit stumped about using the table itself though. I've found the value closest to 0.8 (0.80234) in the body of the table but I'm not sure how to convert this into an actual value - which side of the table should I be reading off? Sorry if this sounds dumb:o:

    No problem.

    Look at the 0.8 on the left and the 0.04 and 0.05 above. You can see that the value you need lies between 0.84 and 0.85.

    I make it about 0.8417. I don't know how accurate you have to be.

    By the way the 0.79955 is closer.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Ah, thanks That makes sense now.
    Offline

    0
    ReputationRep:
    now i have nother Q:
    what about 65% confidence interval?? how do i get the critical value now??
    Offline

    1
    ReputationRep:
    Sorry about the delay...I wasn't ignoring your PM. I just got home after a week away.

    To almost generalise the advice above...

    Subtract from 100%

    100%-65%= 35%

    Divide by 2.

    35 / 2 =17.5%

    Subtract that from 100 and you're looking for 82.5% so on the table you need 0.825
    Offline

    0
    ReputationRep:
    no worries... i've just been lookng for this all over the internet and cant find it for a assignment and i would really wanna know too not just ask someone the answer

    well i know that part.. but where can i find this .825?? in which table?
    Offline

    1
    ReputationRep:
    This one?

    (Original post by windsock)
    I *think* I've found the table you're referring to. Is it Page 24 of this:

    http://www.aqa.org.uk/qual/pdf/FORMULAE.PDF ?

    If it is, I don't suppose you could give me an idea of how to use it:o: , for example how I'd find the critical values for a 60% confidence interval?
    Offline

    0
    ReputationRep:
    hehe i waS just looking in it..
    am i suppose to be looking in table 4? or table 3?

    in table 3 though there are number front left to right and down going.. like 0.00 0.01 ....
    Offline

    0
    ReputationRep:
    ok i understand its suppose to be table 3 page 24...

    now i need p= 0.825 ... so i just found between which and which...

    but now what do that 0. smth mean?? which one do i take???
    Offline

    0
    ReputationRep:
    now i found this..ill attach a pic so ill need hlp with what i found or if i did
    Attached Images
     
    Offline

    0
    ReputationRep:
    ok my bet
    i feel damn now
    i got it now.. its around 0.934
    got it thanx a lot for your help!!!

    now it seems a damn Q lol
 
 
 
Write a reply… Reply
Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. Oops, you need to agree to our Ts&Cs to register
  2. Slide to join now Processing…

Updated: October 31, 2008
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Poll
Do you think you'll achieve your predicted A Level grades?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read here first

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
Study resources

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.