 # Knowing to use 1 or 2 tailed test

Student’s t-Distribution

Level of Significance for One-Tailed Test
df 0.100 0.050 0.025 0.01 0.005 0.0005
Level of Significance for Two-Tailed Test
df 0.20 0.10 0.05 0.02 0.01 0.001
30 1.310 1.697 2.042 2.457 2.750 3.646
40 1.303 1.684 2.021 2.423 2.704 3.551
60 1.296 1.671 2.000 2.390 2.660 3.460
120 1.289 1.658 1.980 2.358 2.617 3.373

From a sample of 41 orders for an on-line bookseller, the average order size is \$75, and the sample standard deviation is \$18. Assume the distribution of orders is normal. For which interval can one be exactly 90% confident that the population mean is contained in that interval?

How am I supposed to know to use the 0.05 aligned with the n-1 df for the level of sig. from the 1 tailed 0.05, rather than the 2 tailed table’s 0.05?

When you are constructing a confidence interval you always use the critical values associated with a two tailed test.

You use one tailed tests in hypothesis testing, when the null hypothesis contains either >= or =<, you use a two tailed test in hypothesis testing if the null contains ≠.

Go to see the Appendices of distribution table of t,
it’s assumed ONE-tailed test. Meaning the level of significance is one-tailed.

Because 90% confidence interval default to TWO tails, but in the t-table we ONLY have ONE-tailed, we divided 10% by 2 to look in 5%(0.05) for One-Tailed Test

If it said the level of significance is a TWO-tailed test, it’s ALREADY calculated for you, so just look at 10%(0.1), which align with one-tailed test

You couldn’t use 0.05 because it said Two-Tailed Test, your two-tails sum up as 0.05, meaning one tail is 0.025, another tail is 0.025, then you are constructing a 95% confidence interval.