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Single Sample t Test
(A worked Problem:  Procedure explained in more detail
in Chapter 12)

Suppose that as a military psychologist you know that the polulation of sonar operators has a mean identification rat of 82 targets out of 100.  You have just developed a nwe sonar training system that, you claim, will increase the number of targets correctly identified.  Using the data from the 15 trainees listed below conduct a single sample t test to determine whether they perform significantly better than the population of sonar operators trained using the traditional method.

      Number of targets correctly identified

88    79    92    87     82    86    91    80     77    83

91    85    82    89     94

I.  First we must state the hypotheses

    A.  The null hypothesis: 
sst1.gif (974 bytes)

    B.  The research hypothesis
        sst2.gif (1142 bytes)

II.  Identify the mean of the population
        sst4.gif (929 bytes)

III.  Compute the mean of the sample
        sst3.gif (990 bytes)

IV.  Compute the standard error of the mean

    A.  Do you have the population standard deviation?

        l.  If yes then use the following formula to compute the standard error of the mean
            sst5.gif (1012 bytes)

        2.  In this case we do not have the population standard deviation and we must
                estimate it using the following formula

            a.   To use this formula we must compute the standard deviation of the sample

                S = 5.147

            b.   Then we divide the standard deviation of the sample by the square root of n-1.



III.  Compute t

        sst8.gif (1537 bytes)

IV.  The significance of t

    A.  Compute the degrees of freedom

        df = n-1 = 15-1 = 14

    B.  Look up critical value in Table T using the column for a one-tail research hypothesis

        C.V. = 1.761

    C.  Conclusion:  Because the computed t, 2.809, is greater than the critical value, 1.761,
            we reject Ho and accept H1.  Therefore t is significant and the new training method
            was significantly better than the traditional training method.           

Copyright 2004 by Mark W. Vernoy