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Thread: Please help! I am failing my stats class and have a few more assignments to help me!

  1. #1
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    Please help! I am failing my stats class and have a few more assignments to help me!

    4.4 Find the p-value. An independent random sample is selected from an approximately normal
    population with an unknown standard deviation. Find the p-value for the given set of hypotheses
    and T test statistic. Also determine if the null hypothesis would be rejected at α = 0.05.

    (a) HA : μ > μ0, n = 11, T = 1.91
    (b) HA : μ < μ0, n = 17, T = −3.45


    (c) HA : μ 6= μ0, n = 7, T = 0.83
    (d) HA : μ > μ0, n = 28, T = 2.13
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  2. #2
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    Re: Please help! I am failing my stats class and have a few more assignments to help

    a) This is a one sided test with the upper tail as the rejection region.

    note that with n=11 (I assume this is the sample size) the number of degrees of freedom $\nu=n-1=10$

    Using a table or software we find (and you can enter the bit in italics directly in at wolframalpha.com)

    p-value = 1-CDF[StudentTDistribution[10]=0.0426

    0.0426 < 0.05 so we would reject the Null hypothesis

    b) This is a one sided test with the lower tail as the rejection region

    See if you can follow what I did in (a) to solve this one. Just use the CDF directly rather than 1-CDF since this is the lower tail.

    c) This is a two tailed test

    We calculate the critical points of the test, $p_{lo},p_{hi}$ for $\alpha =0.05$ such that

    $p_{lo}$ corresponds to probability 0.025, and $p_{hi}$ corresponds to probability 1-0.025 = 0.975

    $p_{lo}$ = InverseCDF[StudentTDistribution[6],0.025] = -2.44691

    $p_{hi}= -p_{lo}= 2.44691$

    we reject if $p_{val} < p_{lo} \vee p_{hi}< p_{val}$

    The p-value for this problem is found as

    p-value =CDF[StudentTDistribution[6],0.83] = 0.780846

    This falls within the acceptance region so we do not reject the null hypothesis

    d) just do what I did in problem (a) with the different numbers
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