CE ABOUT A POPULATION MEAN (a) State the null and alternative hypotheses. Explain why the investigators used a two-sided alternative. bobi (b) Carry out a test and report your conclusion in simple language. (c) The investigators used the test you just carried out. Any use of the t proce- dures with samples of this size is risky. Why? CHAPTER 17 SUMMARY Tests and confidence intervals for the mean u of a Normal population are based on the sample mean x of an SRS. Because of the central limit theorem, the resulting pro- cedures are approximately correct for other population distributions when the sample is large enough. The standardized sample mean is the one-sample z statistic: - I In practice, we rarely know o. We can, however, replace the standard deviation o/n of with the standard error s//n and CH get the one-sample t statistic: d S. - u^/s This t statistic has the t distribution with n - 1 degrees of freedom. There is a t distribution for every positive degrees of freedom. All are symmetre distributions similar in shape to the standard Normal distribution. The t distribution approaches the N(0, 1) distribution as the degrees of freedom increases. Technology (statistical software, graphing calculators, applets) can be used to auto mate the computations, based on the t(n - 1) distribution, required to obtain a co fidence interval for the mean u of a population or to test a set of null and alternative hypotheses about µ. A level C confidence interval for the mean µ of a Normal population is: *干X o col 3. representative sample of a The numerical summary provided suggests that the distribution of blood mer- cury Briefly explain your answer. IWhich of the two issues addressed in parts (a) and (b) would be of greater a concern if we wanted to use a t procedure for these data? . Sitting versus squatting. Squatting for defecation continues to be the tra- dirional position in most of Asia and Africa. In contrast, the practice of sitting voilet seats has proliferated in Western countries since the 19th century with the development of the sewage system. This difference, along with differences in diet, might explain the higher rate of hemorrhoids and constipation in Western countries. A recent study asked if body position affects defecation in humans. Researchers recruited 6 healthy adult volunteers and took X-rays of their intesti- nal systems to measure the anorectal angle (in degrees). Note that, as with a water hose, an angle of 180 degrees should provide the least amount of flow dis- ruption. For each subject, an X-ray was taken once in a sitting position and once in a squatting position. Here are the findings:18 Subject Sitting Squatting orh 601 73 122 1. 2. 117 141 103 Ini Isou 5 98 121 boilar 9. que bobnjaio 125 142 os cougouce