The p-value and rejecting the null (for one- and two-tail tests)

The p-value (or the observed level of significance) is the smallest level of significance at which you can reject the null hypothesis, assuming the null hypothesis is true. You can also think about the p-value as the total area of the region of rejection. Remember that in a one-tailed test, the region of rejection is consolidated into one tail, whereas in a two-tailed test, the rejection region is split between two tails.

Learn mathKrista KingSeptember 13, 2020math, learn online, online course, online math, probability and statistics, probability and stats, probability, statistics, stats, p-value, rejecting the null, one-tail test, two-tail test, upper-tail test, lower-tail test

Calculating test statistics for means and proportions for one- and two-tailed tests

With any hypothesis test, we need to state the null and alternative hypotheses, then determine the level of significance. We’ve already covered these first two steps, and now we want to learn how to calculate the test statistic, which will depend on whether we’re running a two-tail test or a one-tail test.

Learn mathKrista KingMay 23, 2019math, learn online, online course, online math, probability, stats, statistics, probability and statistics, probability and stats, hypothesis testing, inferential statistics, one-tail test, one-tailed test, upper-tail test, lower-tail test, two-tail test, alpha level, alpha value, splitting the alpha, test statistics, population means, means, population proportions, proportions, significance level, level of significance, region of rejection, rejection region, region of acceptance, non-rejection region, z-score, z-table, null hypothesis, accepting the null, accepting the null hypothesis, rejecting the null, rejecting the null hypothesis, standard deviation is known, known standard deviation, standard deviation is unknown, unknown standard deviation, sigma is known, sigma is unknown, large sample, small sample

Type I and II errors and significance level

Type I error rate is the rejecting the null hypothesis when it’s true, and Type II error rate is the probability of accepting the null hypothesis when it’s false. Type I error is called “alpha,” and Type II error is called “beta.”

Online Math Courses

Courses