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Math Help - [SOLVED] how to get the p-value from this t-distribution?

  1. #1
    DoubleCherryPie
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    [SOLVED] how to get the p-value from this t-distribution?

    10.27) In contract negotiations, a company claims that a new incentive scheme has resulted in average weekly earnings of at least $400 for all customer service workers. A union representative takes a random sample of 15 workers and finds that their weekly earnings have an average of $381.35 and a standard deviation of $48.60. Assume a normal distribution. ("Statistics for Business and Economics, Sixth Edition" by Paul Newbold et al.)

    a. Test the company's claim.

    H0: the mean is greater than or equal to 400
    H1: the mean is less than 400

    Okay...so I calculated that t = -1.486, but I don't know where to go from there. From running the T-test program on my calculator I found that the p-value is 0.797, meaning I would reject H0 at alpha levels greater than 7.97%. My question is, how do I solve for this p-value without a calculator program (just using the charts), since I won't be allowed to use calculator programs and statistical tests on my test? THANK YOU!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by DoubleCherryPie View Post
    10.27) In contract negotiations, a company claims that a new incentive scheme has resulted in average weekly earnings of at least $400 for all customer service workers. A union representative takes a random sample of 15 workers and finds that their weekly earnings have an average of $381.35 and a standard deviation of $48.60. Assume a normal distribution. ("Statistics for Business and Economics, Sixth Edition" by Paul Newbold et al.)

    a. Test the company's claim.

    H0: the mean is greater than or equal to 400
    H1: the mean is less than 400

    Okay...so I calculated that t = -1.486, but I don't know where to go from there. From running the T-test program on my calculator I found that the p-value is 0.797, meaning I would reject H0 at alpha levels greater than 7.97%. My question is, how do I solve for this p-value without a calculator program (just using the charts), since I won't be allowed to use calculator programs and statistical tests on my test? THANK YOU!
    You decide what value of p you would reject the null hypotheseis, usualy
    somethig like 0.05, which we look up in a table of the cumulative t-
    distribution (using the nu=14 degrees of freedom line). We may have to do
    this by looking up 0.95, and changing the sign of the result.

    My table gives a critical t-value of -1.76 for this, which means that 95% of
    the time we should see t-values greater than this. Your value is greater than
    this so we cannot reject the hypotheseis that the mean is $400 from this at
    this level.

    RonL
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