统计学CH11 英文版.pptVIP

Developing an Understanding of Statistical Concepts We then compute the test statistic and determine how likely it is to observe this large (or small) a value when the null hypothesis is true. If the probability is small we conclude that the assumption that the null hypothesis is true is unfounded and we reject it. Developing an Understanding of Statistical Concepts When we (or the computer) calculate the value of the test statistic we’re also measuring the difference between the sample statistic and the hypothesized value of the parameter. The unit of measurement of the difference is the standard error. Developing an Understanding of Statistical Concepts In Example 11.2 we found that the value of the test statistic was z = 1.19. This means that the sample mean was 1.19 standard errors above the hypothesized value of. The standard normal probability table told us that this value is not considered unlikely. As a result we did not reject the null hypothesis. The concept of measuring the difference between the sample statistic and the hypothesized value of the parameter in terms of the standard errors is one that will be used frequently throughout this book Probability of a Type II Error It is important that that we understand the relationship between Type I and Type II errors; that is, how the probability of a Type II error is calculated and its interpretation. Recall Example 11.1… H0: μ = 170 H1: μ 170 At a significance level of 5% we rejected H0 in favor of H1 since our sample mean (178) was greater than the critical value of (175.34). Probability of a Type II Error β A Type II error occurs when a false null hypothesis is not rejected. In example 11.1, this means that if is less than 175.34 (our critical value) we will not reject our null hypothesis, which means that we will not install the new billing system. Thus, we can see that: β = P( 175.34 given that the null hypothesis is false) Example 11.1 (revisited) β = P(