**Single Sample t Test
(A worked Problem: Procedure explained in more detail **

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

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 H_{1}. Therefore *t* is significant and the new training
method

was significantly
better than the traditional training
method.

Copyright © 2004 by Mark W. Vernoy