Since n = 15, our test statistic t* has n - 1 = 14 degrees of freedom. Also, suppose we set our significance level α at 0.05, so that we have only a 5% chance of making a Type I error. The P-value for conducting the right-tailed test H 0 : μ = 3 versus H A : μ > 3 is the probability that we would observe a test statistic greater than t* = 2.5 if the population mean \(\mu\) really were 3. Recall that probability equals the area under the probability curve. The P-value is therefore the area under a t n - 1 = t 14 curve and to the right of the test statistic t* = 2.5. That is, since the P-value, 0.0127, is less than \(\alpha\) = 0.05, we reject the null hypothesis H 0 : μ = 3 in favor of the alternative hypothesis H A : μ > 3. Note that we would not reject H 0 : μ = 3 in favor of H A : μ 3 if we lowered our willingness to make a Type I error to \(\alpha\) = 0.01 instead, as the P-value, 0.0127, is then greater than \(\alpha\) = 0.01. #TEST STATISTIC HYPOTHESIS TEST CALCULATOR SOFTWARE#.
0 Comments
Leave a Reply. |