PS 601 Notes – Part II Statistical Tests. Notes Version - March 8, 2005. Statistical tests. We can use the properties of probability density functions to make probability statements about the likelihood of events occurring.
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When we cannot use the population standard deviation, we must employ a different statistical test
Think of it this way:
The sample standard deviation is biased a little low, but we know that as the sample size gets larger, it becomes closer to the true value.
As a result, we need a sampling distribution that makes small sample estimates conservative, but gets closer to the normal distribution as the sample size gets larger, and the sample standard deviation more closely resembles the population standard deviation.
The t-test formula gives you a value that you can compare to the critical value.
Conducting a one-tailed test, if the calculated t-value is greater that the critical value of t, or less than –(critical value of t), we conclude that the sample is significantly different that the population.
Choice of t or –t is determined by the one-tailed test direction.
Note that a t-value that exceeds the critical value means that the probability of that t is less than the selected α-level.