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Math Help - Help me to solve this Hypothesis problem

  1. #1
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    Question Help me to solve this Hypothesis problem

    Past experience indicates that the time for high school seniors to complete standardized test is a normal random variable with a standard deviation of 6 minutes. Test the hypothesis that sigma=6 against the alternative that sigma< 6 if a random sample of 20 high school seniors has a standard deviation s=4.51. Use a 0.05 level of significance.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by fahad View Post
    Past experience indicates that the time for high school seniors to complete standardized test is a normal random variable with a standard deviation of 6 minutes. Test the hypothesis that sigma=6 against the alternative that sigma< 6 if a random sample of 20 high school seniors has a standard deviation s=4.51. Use a 0.05 level of significance.
    This question requires the use of the variance ratio of F-test. The null hypothesis is thst \sigma=6, the 95-th percentile for the
    F-distribution with n_1=\infty and n_2=19
    is 1.88,

    So:

    F=\frac{6^2}{4.51^2}=1.769<1.88

    So our results fail the lower one-tailled test, so we reject the null hypothesis
    in favour of the alternative that \sigma<6.

    You may read more about the F-test here.

    RonL
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