RESEARCH METHODS HANDBOOK

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Contents	Introduction	Descriptive	Hypothesis	Tables	Appendix

Comparing a Population Mean to a Sample Mean
(T-test)

Assumptions

Interval/ratio level data

Random sampling

Normal distribution in population

State the Hypothesis Null Hypothesis (Ho): There is no difference between the mean of the population and the mean of the sample.

Alternative Hypothesis (Ha): There is a difference between the mean of the population and the mean of the sample.

Ha for 1-tail test: The mean of the sample is greater (or less) than the mean of the population.

Set the Rejection Criteria Determine the degrees of freedom = n-1

Determine level of confidence -- alpha (1 or 2-tailed)

Use the t distribution table to determine the critical value

Compute the Test Statistic Standard error of the sample mean

Test statistic

Decide Results of Null Hypothesis There is/is not a significant difference between the mean of one population and the mean of another population from which the sample was obtained.

Example