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Math Help - Critical,Test values

  1. #1
    Newbie sweetkendra's Avatar
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    Question Critical,Test values

    I am having a bit of a problem with this one. Any help will be appreciated.

    A clothing retailer believes that 35% of its customers are between the ages of 20 and 30. A survey of 150 of its customers showed 55 between the ages of 20 and 30. At a 0.10 level of significance, what is the test value? What is the critical value? And Does the data show a contradiction to the retailer's belief?

    This is what I have:
    p=x/n=55/150=0.366 (0.37) p=0.35 q=1-0.35=0.65
    ^
    z=p-p/sq. rt. pq/n= 0.37-0.35/sq tr. (0.35)(0.65)/150=
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sweetkendra View Post
    I am having a bit of a problem with this one. Any help will be appreciated.

    A clothing retailer believes that 35% of its customers are between the ages of 20 and 30. A survey of 150 of its customers showed 55 between the ages of 20 and 30. At a 0.10 level of significance, what is the test value? What is the critical value? And Does the data show a contradiction to the retailer's belief?

    This is what I have:
    p=x/n=55/150=0.366 (0.37) p=0.35 q=1-0.35=0.65
    ^
    z=p-p/sq. rt. pq/n= 0.37-0.35/sq tr. (0.35)(0.65)/150=
    Well I would work with the numbers rather than the proportions.

    Under the null hypothesis (that the retailers belief is true) then the mean
    number of customers in the given range out of 150 is \mu=52.5, and the
    standard deviation is \sigma=\sqrt{150 \times 0.35 \times 0.65} .

    Now we will use the normal approximation to the binomial distribution and
    assume that the number of such customers is normally distributed with mean
    \mu and sd \sigma

    Now we will reject the null hypothesis if p(z>z_obs)<0.05 , where

    z_obs=\frac{mu-54.5}{\sigma}

    (that is we have a one sided test.

    The critical value for this is: \approx 1.645

    RonL
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  3. #3
    Newbie sweetkendra's Avatar
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    Question Critical,Test Values

    Thank you for your help CaptainBlack. But can you explain to me how to find the test value?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by sweetkendra View Post
    Thank you for your help CaptainBlack. But can you explain to me how to find the test value?
    You use a table of the cumulative standard normal distribution to do a
    reverse table look up - if that makes any sense. Alternativly you need
    a peice of technology that will do it for you.

    RonL
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  5. #5
    Newbie sweetkendra's Avatar
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    Smile critical, test values

    Thank bunches. I have the tables needed.
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