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    Null and alternate hypothesis

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    1.A machine produces 5-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows:
    4.94 4.94 5.07 4.91 4.98 5.00 4.94 5.09 5.00 4.92 5.08 5.06
    Assuming that a = 0.10, test the hypothesis that the population mean is equal to 5.
    ?State the null and alternate hypotheses
    ?Calculate the mean and standard deviation
    ?Determine which test statistic applies, and calculate it
    ?Determine the critical value(s).
    ?State your decision: Should the null hypothesis be rejected?

    7. The pulse rates below were recorded over a 30-second time period, both before and after a physical fitness regimen. The data is shown below for 8 randomly selected participants. Is there sufficient evidence to conclude that a significant amount of improvement took place? Assume pulse rates are normally distributed. Test using a = 0.05.
    ?State the null and alternate hypotheses
    ?Calculate the mean and standard deviation
    ?Determine which test statistic applies, and calculate it
    ?Determine the critical value(s).
    ?State your decision: Should the null hypothesis be rejected?
    Before 43 34 37 41 41 59 36 58
    After 37 36 40 49 52 51 31 55
    (Points :10)

    8. You are given the following data. Test the claim that there is a difference in the means of the two groups. Use a = 0.05.
    Group A Group B
    xbar1 = 10 xbar2 = 4
    s1 = 15 s2 = 19
    n1 = 89 n2 = 69
    ?State the null and alternate hypotheses
    ?Determine which test statistic applies, and calculate it
    ?Determine the critical value(s).
    ?State your decision: Should the null hypothesis be rejected?

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    https://brainmass.com/statistics/hypothesis-testing/null-alternate-hypothesis-289337

    Solution Preview

    Please see the attached file.

    1. The null hypothesis to be tested is
    Against the alternative hypothesis
    Given a sample of 12 observations
    Mean = = 4.99
    Variance = = 0.0044
    Standard deviation = = 0.0663

    The test statistic , this statistic follows student's t distribution with n-1 degrees of freedom.
    The calculated value of the test statistic
    From student's t tables with 11 d.f the critical value for  = 0.10 is =1.80

    (Note that this critical value can be obtained by using TINV ...

    Solution Summary

    A null and alternative hypothesis is examined.

    $2.19

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