Worked Problem.....Single Sample t Test.....Psyc205/Soc205.....Vernoy

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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:

B. The research hypothesis

II. Identify the mean of the population

III. Compute the mean of the sample

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

        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

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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 H_o and accept H₁. Therefore t is significant and the new training method
            was significantly better than the traditional training method.