One sided t test

Can someone please explain the one sided t test.

I always end up making mistakes with this.

Thanks.

In a one-tailed t-test you can think about it as looking at one end of the distribution.

Where do you have trouble? Is it picking the appropriate critical value given the measure of reliability (type 1 error rate or confidence level)?

If, for example, you want to have the probability of a type one error (alpha) =0.05 (5%) for a one tailed test, you must notice that the entire probability is in one tail-- therefore, your critical value will be the same as if you were doing a 2-tailed test at an alpha of 0.10 (90% Confidence) doing the 2-tailed test at 0.10 means 0.05 is the probability in each tail. Let me know if this helped!

Take a look at this (or another) t-table and see if this helps now http://faculty.vassar.edu/lowry/PDF/t_tables.pdf

Before looking at t-table, always ask a question. is this one tailed or two tailed?

If you null hypothesis includes ‘<=’ or ‘>=’ then its one tailed test.

If it contains only ‘=’ sign, its two tailed test.

I’ve missed this many times. I hope I remember in exam.

No I have trouble finding out whether to reject the null or fail to reject the null.

If your calculated test statistic is greater in magnitude than the critical value from the table (or if the p-value is smaller than the alpha{significance level}) then you reject the null hypothesis. In the opposite case you fail to reject the null hypothesis. This is for any hypothesis test-- not just one-tailed tests.

If your null hypothesis is XXh (X-hypothesized), then:

  • Find the t-critical value for your level of significance α. Remember the the t-critical value for a one-tailed t-test at α is the same as the t-critical value for a two-tailed t-test at 2α. This t-critical will be positive.
  • Compute your test statistic (for the mean it’ll be (X-bar – Xh)/sX, where sX is the sample std. dev. of X).
  • If the test statistic is greater than t-critical, reject the null hypothesis; if not, fail to reject the null.

If your null hypothesis is XXh, then:

  • Find the t-critical value for your level of significance α. This t-critical will be negative.
  • Compute your test statistic,
  • If the test statistic is less than t-critical, reject the null hypothesis; if not, fail to reject the null

Thanks. It’s helpful.

You’re quite welcome. I’m glad that it was.

Can you please explain this sentence: “…thicker tails mean more observations away from the center of the distribution (more outliers). Hence, hypothesis testing using the t-distribution makes it more difficult to reject the null relative to hypothesis testing using the z-distribution.” Does it mean that, with the same calculated test statistics value, t-test would result in a greater p-value, and thus it’s harder for it to be less than the significant level?

Can you please explain this sentence: “…thicker tails mean more observations away from the center of the distribution (more outliers). Hence, hypothesis testing using the t-distribution makes it more difficult to reject the null relative to hypothesis testing using the z-distribution.” Does it mean that, with the same calculated test statistics value, t-test would result in a greater p-value, and thus it’s harder for it to be less than the significant level?