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    How to Perform a T-test, Sample T and ANOVA

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    Make up statistics to show how the following tests are performed and plotted in a chart:

    Independent Sample T,
    Dependent Sample T,
    One-way ANOVA with LSD,
    Two-way ANOVA

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    Solution Preview

    Please see the attached files.

    t-Test Question.

    The management of white Industries is considering a new method of assembling its three-wheel golf cart. The present method requires 42.3 minutes on the average to assemble a cart. The new method was introduced, and a time and motion study was conducted on a random sample of 24 carts. The mean assembly time was computed to be 40.6 minutes. The standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can it be said that the assemble time under the new method is significantly less than before?

    Note: When you are asked to test if the population mean is equal(not equal )to some value, but the sample is small and you don't know the population standard deviation, then you need to use t-test.
    Solution. We can set up the hypotheses as follows.
    We can use t-test. By a formula , we can compute the test statistic as follows.
    Note: are sample mean, standard deviation and sample size, respectively. So,

    Note that the degree of freedom is n=1=24-1=23
    So, we can compute the p-value

    So, we have to reject the null hypothesis H0: . We conclude that at the .10 level of significance, the assemble time under the new method is significantly less than before.
    Independent Sample Test Question

    Two boats, the Prada (Italy) and the Oracle (USA), are competing for a spot in the upcoming America's Cup race. They race over a part of the course several times. Below are the sample times in minutes. At the .05 significance level, can we conclude that there is a difference in their mean times?

    BoatTime (minutes)

    Prada 12.9 12.5 11.0 13.3 11.2 11.4 11.0 12.3 14.2 11.3
    Oracle 14.1 14.1 14.2 17.4 15.8 16.7 16.1 13.3 13.4 13.6 10.8 ...

    Solution Summary

    The solution invents data on which it performs 5 different kinds of tests, with charts plotted. Attached as Word and Excel.