STA 6166 UNIT 2 Section 1
|Welcome||<||Begin||<||Unit 2||<||Section 1||>||Section 1 Exercises|
|Readings||Ott and Longnecker,Chapter 5, pages 192-262.|
Chapter 5 is fairly long and very dense. You will need to take it in stages. First read about estimation and confidence intervals (sections 5.1-5.3). Note that there is a difference between a point estimate of the mean of the population based on sample data and the interval estimate. Remember that the confidence interval is produced by a set of end points, the upper and lower bounds, that specify the range of possible values for the true, but unknown, population mean. What we are saying is that if we had a large number of sample sets, each set having the same number of randomly selected individuals, then if we compute the confidence intervals for each sample set using the equation on page 200, then we would expect the specified fraction of these confidence intervals to actually contain the true mean. Look at figure 5.4 and attempt the optional activities to get a better idea of what this means. It is important that you have a firm grasp of what a confidence interval is saying. Finally, note that we simply turn the confidence interval equation around in order to estimate the sample size needed to meet our target confidence level (page 205).
If you talk to some of your colleagues who understand statistics a little better, they will tell you that statistical testing (section 5.4) is going out of style, instead you should be computing p-values (section 5.6). Even if you don't formally do statistical tests, you need an understanding of statistical testing if you are to understand p-values. Pay special attention to Type I, Type II and Power definitions. These are terms you constantly find in the research literature. They are used to specify the conditions of the test and the confidence you will have in the conclusions. Finally, like confidence intervals, statistical tests can be turned around to allow calculation of the sample size needed to meet confidence targets(section 5.5).
In the first part of this section, we make the assumption that the true population standard deviation is known. In practice, we rarely know the value of this parameter, hence we have to use our sample data to estimate it. This has ramifications for the statistical test as well as power and sample size computations. With a minor modification, a new statistical test is available ( section 5.7).
Beginning with the bottom of page 235 to 238, there is a discussion about what happens to actual Type I and Type II errors when the data come from distributions that are not symmetric. This leads to an alternative way of testing the center of a population using the median. The Sign Test presented here is just one of a number of alternative test developed by statisticians over the years to handle the case where the data come for a non-normal distribution.
|PPT Lecture||One Sample Mean Inference(PowerPoint, PDF notes)|
|Exercises||To check your understanding of the readings and practice these concepts and methods, go to Unit 2 Section 1 Exercises, do the exercises then check your answers from the page provided. Following this continue on to Section 2.|