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    Computing value of test statistic

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    Consider the following hypothesis test:

    Ho: u > 20 (( their is a line under this sine >))
    Ha: u < 20
    A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.
    a. Compute the value of the test statistic.
    b. What is the p-value?
    c. Using a = .05, what is your conclusion?
    d. What is the rejection rule using the critical value? What is your conclusion?

    And

    Consider the following hypothesis test:
    Ho: u = 22
    Ha: u =22 ( their is a line throw the = sine hare )

    A sample of 75 is used and the population standard deviation is 10. Compute the p-value
    and state your conclusion for each of the following sample results. Use a = .01.
    a. i = 23
    b. i = 25.1
    c. i = 20.

    © BrainMass Inc. brainmass.com October 3, 2022, 12:28 am ad1c9bdddf
    https://brainmass.com/statistics/hypothesis-testing/computing-value-test-statistic-539518

    SOLUTION This solution is FREE courtesy of BrainMass!

    A) this is one tailed z test, since population standard deviation is known
    z (19.4-20)/(2/sqrt(50)) -2.121320344

    B)
    P 0.016947427

    C) since P value is less than 0.05, we reject Ho

    D)
    Critical z value -1.644853627
    Based on the test, we could conclude that the sample mean is less than 20.

    Q2
    Since population standard deviation is known, we use z test.
    Meanwhile, this is a two tailed test.

    a)
    Z 0.866025404
    P value 0.386476231
    We fail to reject Ho since P value is larger than 0.01
    There is insufficient evidence to conclude that the sample mean is not equal to 22.

    b)
    z 2.684678752
    P value 0.007259955
    We reject Ho since P value is less than 0.01
    There is sufficient evidence to conclude that the sample mean is different from 22.

    c)
    z -1.732050808
    P 0.083264517
    We fail to reject Ho since P value is larger than 0.01
    There is insufficient evidence to conclude that the sample mean is different from 22.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com October 3, 2022, 12:28 am ad1c9bdddf>
    https://brainmass.com/statistics/hypothesis-testing/computing-value-test-statistic-539518

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