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t distribution vs z distribution

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    ReputationRep:
    I am working out confidence intervals and was wondering what effect knowing the variance of the distribution has on the interval.
    I know that if i know the variance I am going to use the z distribution as opposed to the t distribution but why would it make a difference on the confidence intervals and which one would i prefer to use??

    any help appreciated!!
  2. Offline

    ReputationRep:
    In general (I'm tempted to say "always"), the more details you know about a set of data, the stronger your confidence about any claims you make.
    The t distribution curve has a similar shape to the Z curve (both bell-shaped) but is flatter (i.e. has "more" probability at the extremes). Have a look at wikipedia.
    What impact do you think that will have on confidence intervals?
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    sof the t disttttbuion curve is flatter, then the confidence intervals will be wider, but why then would i be using the t distribution for the first one, could i not use the z distribution for both?
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    (Original post by masterasg)
    sof the t disttttbuion curve is flatter, then the confidence intervals will be wider, but why then would i be using the t distribution for the first one, could i not use the z distribution for both?
    the first one? both?
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    i guess im trying to ask why cant you use the z distribution for both if the variance is known and not known...
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    Because those are different situations. The theoretical model upon which the normal distribution is based requires the variance of the population to be known, whereas the model the t distribution is built on only requires an estimate of the population variance from a sample of known size.

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