Special Issues in Semiconductor Manufacturing Eecs 290h Fall 2005 Problem Set No. 4 Official Solutions

1. Answer the following questions (briefly explain your answers) a) What is a "test statistic" in the context of Hypothesis testing? A test statistic is the "score" one calculates from the data. Usefull test statistics follow known, well defined distributions under the null, and possibly known distribution(s) under the alternative hypothesis. The test consists of seeing how likely it is, that the test statistic actually came from the null hypothesis distribution. b) How is the power of a test related to the sample size of a test, assuming that the test statistic is an average of independent samples, and it follows the normal distribution? The power of the test should be proportional to the square root of the sample size. This is because the two distributions (the null and the alternate) will reduce their variance at one over the square root of the sample size. c) Is the power (P) of a test independent of the type I error? No. One can trade power for type one error and vice versa. The power of the test depends on the criterion for Ho rejection, and this criterion (limit) is directly dependent on the type I error a.