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Chapter 8: Hypothesis Tests for a Single Variable Y 217 Hypothesis testing may result in wrong decisions. The probability that the null hypothesis is rejected when in fact it is true is called (alpha). The probability that the alternative hypothesis is wrongly rejected is called (beta). The significance level of a hypothesis test is . The significance level is used as an accept/reject threshold for the null hypothesis. The p-value is a number between 0 and 1. It measures how much the test statistic supports the assumption that the null hypothesis is true. A p-value less than the significance level results in a rejection of the null hypothesis. Using the p-value in the decision rule is a method to accept or reject the null hypothesis. Instead of the p-value and , you can use the test statistic and the critical value in a decision rule to accept or reject the null hypothesis. Critical values define acceptance and rejection regions for the test statistic. These correspond in one-sided alternative hypotheses to this decision rule: Accept H 0 if p . Reject H 0 if p < . Hypothesis tests with two-sided alternative hypotheses can be performed using confidence intervals. For a 5% significance level, use a 95% confidence interval. If the hypothesized population characteristic is within the confidence interval range, accept the null hypothesis; otherwise reject it. Sample sizes that yield hypothesis tests with error probability and need to be calculated before data are collected. The required sample size also depends on how small the difference to detect is. A small difference, relative to the population standard deviation, requires a large sample. Sample sizes can be calculated in JMP using the DOE platform. Power curves are used to examine the trade-offs between sample size, difference to detect, alpha, and power. 8.4 Problems 1. For each of the following situations, set up the null and alternative hypotheses. Using a bell-shaped curve with the null hypothesis value for the mean, sketch the critical region and show the associated as the area under the bell-shaped curve. Schmee, Josef, and Jane Oppenlander. JMP® Means Business: Statistical Models for Management. Copyright © 2010, SAS Institute Inc., Cary, North Carolina, USA. ALL RIGHTS RESERVED. For additional SAS resources, visit support.sas.com/publishing.