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Math Help - significance level

  1. #1
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    significance level

    A company advertises that its program increases a personís overall GAMSAT (Graduate Australian Medical School Admissions Test) score by an average of 15 points. To test this claim, an experiment is set up whereby eight subjects are given a diagnostic test that predicts GAMSAT performance, they then take the program, and finally they take the GAMSAT. A predicted score and actual score are recorded for each subject, with the results given in the table below. Test the validity of the companyís claim at a significance level of a = 0.05.

    Subject Predicted Score Actual Score
    1 50 67
    2 84 96
    3 74 90
    4 67 82
    5 88 95
    6 70 83
    7 57 73
    8 71 83
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  2. #2
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    Quote Originally Posted by wik_chick88 View Post
    A company advertises that its program increases a personís overall GAMSAT (Graduate Australian Medical School Admissions Test) score by an average of 15 points. To test this claim, an experiment is set up whereby eight subjects are given a diagnostic test that predicts GAMSAT performance, they then take the program, and finally they take the GAMSAT. A predicted score and actual score are recorded for each subject, with the results given in the table below. Test the validity of the companyís claim at a significance level of a = 0.05.

    Subject Predicted Score Actual Score
    1 50 67
    2 84 96
    3 74 90
    4 67 82
    5 88 95
    6 70 83
    7 57 73
    8 71 83
    Can you use a paired t-test?
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    ok i think i have done the t-test right. i got:
    t = 0.892409614 BUT i disregarded the negative from the difference of the means (the mean of X1 was less than the mean of X2) is this right??? now what do i do with the significance level of a = 0.05?
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  4. #4
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    Quote Originally Posted by wik_chick88 View Post
    ok i think i have done the t-test right. i got:
    t = 0.892409614 BUT i disregarded the negative from the difference of the means (the mean of X1 was less than the mean of X2) is this right??? now what do i do with the significance level of a = 0.05?
    Define D_i = X_{2i} - X_{1i} for i = 1, .....8, the differences between the observations within each pair.

    Calculate the mean \bar{D} = \frac{1}{8} \sum_{i=1}^{8} D_i and the standard deviation S_D^2 = \frac{1}{8-1} \sum_{i=1}^{8} (D_i - \bar{D})^2 and use the appropriate one sample procedure to complete the inference:

    H_0: ~ \mu_D = 0
    H_1: ~ \mu_D > 0

    Assuming the differences follow a normal distribution:

    t = \frac{\bar{D} - 0}{S_D/\sqrt{8}} = \, ....

    Use tables to get the critical the critical value of t etc.

    You must have examples from class notes or textbook to follow?
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