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Math Help - Hypothesis testing normal distribution

  1. #1
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    Hypothesis testing normal distribution

    Hi I'm doing a further maths AS level (UK high school qualification) and I'm doing a module on statistics.

    My problem lies with mean population hypothesis testing. A normal distribution is assumed, and I'm using the method illustrated in the following example (taken from an answer scheme):

    N(355,52^2)

    Null Hypothesis: mu=355
    Alternative Hypothesis: mu =/= 355 (2-tail test) (=/= is not equal btw :P)

    Test statistic= (344-355)/(52/sqrroot(25)) where 344 is the observed value and 25 is the total number of things in the sample I'm testing.

    I'm then told to compare the test statistic to the critical value of z (I don't really know what this is)

    So in the example the answer says to compare the test statistic to the 5% level 2 tailed critical value of z which equals 1.96.

    Now I know this z thing has something to do with the inverse normal tables, but my question is how do you get the critical value of z from the inverse normal tables?

    How, in the example, did the value of 1.96 come about?

    Thanks!

    The inverse normal table I'm talking about:

    page 22 of http://www.mei.org.uk/files/pdf/formula_book_mf2.pdf
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  2. #2
    Grand Panjandrum
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    Re: Hypothesis testing normal distribution

    Quote Originally Posted by Goatfluff View Post
    Hi I'm doing a further maths AS level (UK high school qualification) and I'm doing a module on statistics.

    My problem lies with mean population hypothesis testing. A normal distribution is assumed, and I'm using the method illustrated in the following example (taken from an answer scheme):

    N(355,52^2)

    Null Hypothesis: mu=355
    Alternative Hypothesis: mu =/= 355 (2-tail test) (=/= is not equal btw :P)

    Test statistic= (344-355)/(52/sqrroot(25)) where 344 is the observed value and 25 is the total number of things in the sample I'm testing.

    I'm then told to compare the test statistic to the critical value of z (I don't really know what this is)

    So in the example the answer says to compare the test statistic to the 5% level 2 tailed critical value of z which equals 1.96.

    Now I know this z thing has something to do with the inverse normal tables, but my question is how do you get the critical value of z from the inverse normal tables?

    How, in the example, did the value of 1.96 come about?

    Thanks!

    The inverse normal table I'm talking about:

    page 22 of http://www.mei.org.uk/files/pdf/formula_book_mf2.pdf
    1. Using the left hand table
    You find the entry in the body of the table that says 0.975, and read off the correcsponding z value that will give this cumulative probability.

    If the value did not occur exactly you would either choose the closest value that does occur or interpolate in the table to get the required point.

    2. Using the right hand table
    Look up the z value for 0.975 (the values in the body of the table are z values.

    We are using 0.975 because the critical value of z cuts off an area of 0.975 to its left, but you want the two sided case with 0.025 above and 0.025 below the cut offs, but these are symmetric.

    CB
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