Intro Stats Lec 17B, 2-Tailed Tests w/ Confidence Ints, Significance Levels, Critical z's, P Values

(0:00) Adrian Peterson has a lot of zero or negative yardage plays, but he makes up for those with a lot of long runs. (1:14) Using confidence intervals to do two-tailed tests of significance. (2:33) Housing spending example where the realtor has no idea whether the parameter value is less than or greater than the null value. (3:53) Start to compute 95% confidence interval for estimating mu. (4:52) Elaborate on the meaning of the level of significance and its relationship to the P-value. (5:22) Finish the computation of the C.I. (7:52) Decision about whether to reject the null hypothesis or not (relate to the statement on the slide). (9:39) Reminder that some people always do two-sided tests just to make themselves have a higher standard of evidence before rejecting the null (since the P-value will end up larger than for a one-sided test). (10:31) Subtleties about P-values, alpha (the level of significance), and real life decisions. (12:59) Choosing alpha first can help you decide whether to reject the null or not just based on the value of z (without computing a P-value): Is it in the "critical region" or not? That is, is it past the "critical value(s)" or not? (13:40) Compute critical value of z = 2.33 for a right-tailed test with alpha = .01. (17:08) Corresponding critical value of z = -2.33 for a left-tailed test with alpha = .01. (17:37) Compute critical value of z = plus or minus 2.575 for a two-tailed test with alpha = .01 (actually, plus or minus 2.576 is a bit closer, but don't worry about it). (19:56) You should be able to calculate and use a P-value as well, as well as consider other real-life factors. (21:01) More information about P-values. (21:25) The usual perspectives to have and language to use in summarizing conclusions of a hypothesis test (a researcher hoping to convince people in the truth of an alternative hypothesis, a prosecuting attorney hoping to convict a defendant). (22:57) How should we make our final decision? Real-life considerations. (25:39) Additional advice: look for outliers, trends, look at graphs, confidence intervals before tests of significance, look out for poorly designed experiments. (26:49) Introduction to the Power of a Test, Type I Errors, and Type II Errors.