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    Historically the average age of European soccer players is reported as 26 years with a standard deviation of 4 years. A random sample of 81 European professional soccer players has an average age of 27 years. We would like to decide if there is enough evidence to establish that average age of European soccer players has increased significantly. What is the decision at ?=.05 and 0.01? Indicate which test you are performing; show the hypotheses, the test statistic and the critical values and mention whether one-tailed or two-tailed.

    © BrainMass Inc. brainmass.com December 24, 2021, 10:19 pm ad1c9bdddf
    https://brainmass.com/statistics/hypothesis-testing/hypothesis-testing-mean-462803

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    Answer
    Since the population standard deviation is known, we can use z test for mean.
    We are testing whether the average age of European soccer players has increased significantly. Hence the test is one-tailed and is an upper tailed test.
    The null hypothesis tested is
    H0: Average age of European soccer players ≤ 26 years. (µ ≤ 26)
    The alternative hypothesis is
    H1: Average age of European soccer players > 26 years. (µ > 26)
    The test statistic used is , where =27, n = 81,  = 4
    Therefore, = 2.25
    When significance level, α = 0.05
    Rejection criteria: Reject the null hypothesis, if the calculated value of test statistic is greater than the critical value at the 0.05 significance level.
    Upper critical value = 1.644853627
    Conclusion: Reject the null hypothesis, since the calculated value of test statistic is greater than the critical value. The sample provides enough evidence to support the claim that the average age of European soccer players has increased significantly.
    Details
    Z Test of Hypothesis for the Mean

    Data
    Null Hypothesis = 26
    Level of Significance 0.05
    Population Standard Deviation 4
    Sample Size 81
    Sample Mean 27

    Intermediate Calculations
    Standard Error of the Mean 0.444444444
    Z Test Statistic 2.25

    Upper-Tail Test
    Upper Critical Value 1.644853627
    p-Value 0.012224473
    Reject the null hypothesis

    When significance level, α = 0.01
    Rejection criteria: Reject the null hypothesis, if the calculated value of test statistic is greater than the critical value at the 0.01 significance level.
    Upper critical value = 2.326347874
    Conclusion: Fails to reject the null hypothesis, since the calculated value of test statistic is less than the critical value. The sample does not provide enough evidence to support the claim that the average age of European soccer players has increased significantly.
    Details
    Z Test of Hypothesis for the Mean

    Data
    Null Hypothesis = 26
    Level of Significance 0.01
    Population Standard Deviation 4
    Sample Size 81
    Sample Mean 27

    Intermediate Calculations
    Standard Error of the Mean 0.444444444
    Z Test Statistic 2.25

    Upper-Tail Test
    Upper Critical Value 2.326347874
    p-Value 0.012224473
    Do not reject the null hypothesis

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

    © BrainMass Inc. brainmass.com December 24, 2021, 10:19 pm ad1c9bdddf>
    https://brainmass.com/statistics/hypothesis-testing/hypothesis-testing-mean-462803

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