Statistics: Difference between results from doing a confidence interval and from doing a t-test?

ANSWER: A Confidence Interval describes the probability that a sample mean will be equal to a value within the Interval. A 95% Confidence Interval is 95% probability that a sample mean will have a value within the Interval. If 95% Confidence Interval = [1, 5] then a sample mean that a Statistician measures will have 95% probability of a value within the Interval [1, 5].

A t-test is the probability that the sample mean matches up to the Table of values. A t-test for a sample size 5 (4 degrees of freedom) has a computed "Standard Value" of 2.1 which has the "look-up" Table a probability of 5.1% (0.051) is larger than alpha = 0.05. The t-test shows the sample mean matches up to the Table of values.

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