Selected Critical Values of the
t-Distribution
A test is 2-tailed if you ask the
question, 'does population 1 differ from population
2'. Then, if the mean for population 1 is significantly
greater or smaller than that for population
2, you reject the null hypothesis. If you ask simply,
is the true mean for population 1 greater than
that for population 2, then you reject the null
hypothesis only if the experimental mean for population
1 is found to be significantly greater. It can
be significantly smaller, but you weren't asking
that question. That would be a one-tailed test.
For a two-tailed test if the calculated value of
t exceeds the tabled value, then report the p value
in the table. For a one-tailed test, the p value
is divided by two. So 'p < 0.05' becomes 'p < 0.025."
The table should include values for
p=0.1 so that a one-tailed test can be conducted
at the p=0.05 level, but we never do such tests
in my class, so why clutter up the table?

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