Chapter08 DRAWING INFERENCES FROM LARGE SAMPLES：PROPORTION.pptVIP

Keller: Stats for Mgmt Econ, 7th Ed Copyright ? 2006 Brooks/Cole, a division of Thomson Learning, Inc. Chapter 12 Inference About A Population Inference About A Population… Identify the parameter to be estimated or tested. Specify the parameter’s estimator and its sampling distribution. Derive the interval estimator and test statistic. Inference About A Population… We will develop techniques to estimate and test three population parameters: Population Mean Population Variance Population Proportion p Inference With Variance Unknown… Previously, we looked at estimating and testing the population mean when the population standard deviation ( ) was known or given: But how often do we know the actual population variance? Instead, we use the Student t-statistic, given by: Inference With Variance Unknown… When is unknown, we use its point estimator s and the z-statistic is replaced by the the t-statistic, where the number of “degrees of freedom” , is n–1. Testing when is unknown… When the population standard deviation is unknown and the population is normal, the test statistic for testing hypotheses about is: which is Student t distributed with = n–1 degrees of freedom. The confidence interval estimator of is given by: Example 12.1… Will new workers achieve 90% of the level of experienced workers within one week of being hired and trained? Experienced workers can process 500 packages/hour, thus if our conjecture is correct, we expect new workers to be able to process .90(500) = 450 packages per hour. Given the data, is this the case? Example 12.1… Our objective is to describe the population of the numbers of packages processed in 1 hour by new workers, that is we want to know whether the new workers’ productivity is more than 90% of that of experienced workers. Thus we have: H1: 450 Therefore we set our usual null hypothesis to: H0: = 450 Example 12.1… Our test statistic is: With n=50 data poi