Explore BrainMass

Explore BrainMass

    Hypothesis Testing of Mean

    Not what you're looking for? Search our solutions OR ask your own Custom question.

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

    System data for a job shop revealed that the average time spent by a job in the shop was approximately n = 5 working days. A random sample of size five is taken with time spent in the shop, 3.7, 4.6, 3.9, 4.1, and 3.8. Is the output consistent with system behavior? (Why?). Construct a statistical test using a level of significance of alpha = 0.05

    © BrainMass Inc. brainmass.com December 24, 2021, 10:06 pm ad1c9bdddf
    https://brainmass.com/statistics/hypothesis-testing/statistical-testing-level-significance-443180

    SOLUTION This solution is FREE courtesy of BrainMass!

    Please see the attachments.

    Statistical testing using a level of significance
    System data for a job shop revealed that the average time spent by a job in the shop was approximately n = 5 working days. A random sample of size five is taken with time spent in the shop, 3.7, 4.6, 3.9, 4.1, and 3.8. Is the output consistent with system behaviour? (Why?). Construct a statistical test using a level of significance of alpha = 0.05
    Answer
    The null hypothesis tested is
    H0: Average time spent by the job in the shop = 5 working days (µ = 5)
    The alternative hypothesis is
    H1: Average time spent by the job in the shop ≠ 5 working days (µ ≠ 5)
    Significance level = 0.05
    Test Statistic used is . Given that = 4.02, n = 5, s = 0.356370594 (Please see the excel sheet)
    Therefore, = -6.14906689
    Decision rule: Reject the null hypothesis, if the absolute value of calculated test statistic is greater than the critical value of t with 4 d.f. at the significance level 0.05.
    Lower critical value = -2.776445105
    Upper critical value = 2.776445105
    Conclusion: Reject the null hypothesis, since the absolute value of calculated test statistic is greater than the critical value. The sample provides enough evidence to conclude that average time spent by a job in the shop is different from 5 working days. Hence the output is not consistent with system behaviour.
    Details
    t Test for Hypothesis of the Mean

    Data
    Null Hypothesis = 5
    Level of Significance 0.05
    Sample Size 5
    Sample Mean 4.02
    Sample Standard Deviation 0.356370594

    Intermediate Calculations
    Standard Error of the Mean 0.159373775
    Degrees of Freedom 4
    t Test Statistic -6.14906689

    Two-Tail Test
    Lower Critical Value -2.776445105
    Upper Critical Value 2.776445105
    p-Value 0.003547921
    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, 10:06 pm ad1c9bdddf>
    https://brainmass.com/statistics/hypothesis-testing/statistical-testing-level-significance-443180

    Attachments

    ADVERTISEMENT