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Confidence Intervals and Critical Values

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    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)
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    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.
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    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?
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    (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.
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    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:
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    (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.
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    Ah, thanks That makes sense now.
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    now i have nother Q:
    what about 65% confidence interval?? how do i get the critical value now??
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    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
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    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?
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    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?
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    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 ....
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    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???
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    now i found this..ill attach a pic so ill need hlp with what i found or if i did
    Attached Thumbnails
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    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

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Updated: October 31, 2008
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