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    Parametric vs. Non-parametric Testing

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    Gerber Biotech Industries was testing three different drugs namely Breath-Easy, Fresh Mint and Sober Breath, meant for neutralizing the alcohol content in the breath so that the (drunken) drivers can pass the breath analyzer test. The three drugs are tested on randomly selected volunteers and the time taken for each of the drugs to neutralize the effect is recorded. Breath-Easy and Fresh Mint were tested on 8 individuals. The data is presented in the table below:
    Volunteer Number
    Drug 1 2 3 4 5 6 7 8
    Time Taken in Minutes
    BE 35 51 56 57 60 74
    FM 43 53 41 57 36 55
    SB 35 32 28 44 40 34 73 48

    (a) Test whether there is any significant difference between the average time taken by the three drugs using an appropriate parametric test (Use 0.10 percent significance level)

    (b) Repeat the test using an appropriate non-parametric test.

    (C) Should the conclusions between the two tests consistent? Why or why not? If the conclusions are not consistent, which one would you agree with and why?

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    Solution Preview

    The problem is solved using One-way ANOVA and KRUSKAL WALLIS TEST.
    (a) Test whether there is any significant difference between the average time taken by the three drugs using an appropriate parametric test (Use 0.10 percent significance level)
    This is a question on comparing more than 2 means and ANOVA is the parametric test to be used for this test.
    Hypothesis:
    H0: Three populations are identical
    H1: atleast one of the 3 populations is different from others
    Calculate F-statistics using the data and following degrees of freedom.
    dfC=3-1=2
    dfE=6+6+8-3=17
    dfT=6=6+8-1=19

    F=MSC/MSE=324.15/152.38=2.13

    F Critical from table at DOF in ...

    Solution Summary

    This solution conducts a statistical analysis the data of the three different drugs created by the Gerber Biotech Industries with a one-way ANOVA and Kruskal Wallis Test. For each test, a null and alternative hypothesis is provided and either a F-statistic or F_j is calculated and compared to the p-value to make a decision in accepting or rejecting the null hypothesis.

    $2.19

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