Do the data support the conjecture that progabide reduces the mean number of

6.65 Refer to Exercise 6.64. The small number of vehicles in the study has led to criticism of the results. A new study is to be conducted with a larger sample size. Assume that the populations of damages are both normally distributed with a common s ⫽ 700.

a. Determine the sample size so that we are 95 confident that the estimate of the

difference in mean repair cost is within 500 of the true difference.

b. For the research hypothesis H

a : m SUV ⬎ m MID , determine the sample size required to obtain a test having a ⫽ .05 and bm d ⬍ .05 when m SUV ⫺ m MID ⱖ 500. Law 6.66 The following memorandum opinion on statistical significance was issued by the judge in a trial involving many scientific issues. The opinion has been stripped of some legal jargon and has been taken out of context. Still, it can give us an understanding of how others deal with the problem of ascertaining the meaning of statistical significance. Read this memorandum and com- ment on the issues raised regarding statistical significance. Memorandum Opinion This matter is before the Court upon two evidentiary issues that were raised in anticipation of trial. First, it is essential to determine the appropriate level of statistical significance for the admission of scientific evidence. With respect to statistical significance, no statistical evidence will be admitted dur- ing the course of the trial unless it meets a confidence level of 95. Every relevant study before the court has employed a confidence level of at least 95. In addition, plaintiffs concede that social scientists routinely utilize a 95 confidence level. Finally, all legal authorities agree that statistical evidence is inadmissable unless it meets the 95 confidence level required by statisticians. Therefore, because plaintiffs ad- vance no reasonable basis to alter the accepted approach of mathematicians to the test of statistical significance, no statistical evidence will be admitted at trial unless it satisfies the 95 confidence level. Env. 6.67 Defining the Problem 1. Lead is an environmental pollutant especially worthy of at- tention because of its damaging effects on the neurological and intellectual development of children. Morton et al. 1982 collected data on lead absorption by children whose parents worked at a factory in Oklahoma where lead was used in the manufacture of batteries. The con- cern was that children might be exposed to lead inadvertently brought home on the bodies or clothing of their parents. Levels of lead in micrograms per deciliter were measured in blood samples taken from 33 children who might have been exposed in this way. They constitute the Exposed group. Collecting Data 2. The researchers formed a Control group by making matched pairs. For each of the 33 children in the Exposed group they selected a matching child of the same age, living in the same neighborhood, and with parents employed at a place where lead is not used. The data set LEADKIDS contains three variables, each with 33 cases. All involve measure- ments of lead in micrograms per deciliter of blood. c1 Exposed Leadmgdl of whole blood for children of workers in the battery factory c2 Control Leadmgdl of whole blood for matched controls c3 Diff The differences: Exposed - Control. Mann–Whitney Confidence Interval and Test Midsize N 8 Median 11.69 SUV N 8 Median 13.59 Point estimate for ETA1–ETA2 is 2.32 95.9 Percent CI for ETA1–ETA2 is 14.83, 0.33 W 48.0 Test of ETA1 ETA2 vs ETA1 ETA2 is significant at 0.0203 These data are listed next. This is necessarily an observational study rather than a controlled experiment. There is no way that the researchers could have assigned children at random to parents in or out of lead- related occupations. Furthermore, the Exposed subjects were all chosen from the small group of children whose parents worked at one particular plant. They were not chosen from the larger population of children everywhere who might be exposed to lead as a result of their parents’ working conditions. If lead levels are unusually high in the Exposed group, it might be argued that the lead in their blood came from some source other than their parents’ place of work: from lead solder in water pipes at home, from lead-paint dust at school, from air pollution, and so on. For this reason a properly chosen control group of children is crucial to the credibility of the study. In principle, the children in the Control group should be subject to all of the same possible lead contaminants as those in the Exposed group, except for lead brought home from work by parents. In practice, the designers of this study chose to use two criteria in forming pairs: neighborhood and age. Neighborhood seems a reasonable choice because general envi- ronmental conditions, types of housing, and so on could vary greatly for children living in different neighborhoods. Controlling for age seems reasonable because lead poisoning is largely cumulative, so levels of lead might be higher in older children. Thus for each child in the Exposed group, researchers sought a paired child of the same age and living in the same neighborhood. Complete Listing of Dataset LEADKIDS Complete Listing of Dataset LEADEXP Exposed Control Diff Lead JobExp JobHyg 38 16 22 14 3 1 23 18 5 13 3 1 41 18 23 25 3 1 18 24 -6 39 2 1 37 19 18 41 3 2 36 11 25 18 3 2 23 10 13 49 3 2 6 2 15 47 29 2 2 31 16 15 16 1 2 34 18 16 38 3 3 24 18 6 23 3 3 14 13 1 37 3 3 21 19 2 62 3 3 17 10 7 24 3 3 16 16 0 45 3 3 20 16 4 39 3 3 15 24 -9 48 3 3 10 13 -3 44 3 3 45 9 36 35 3 3 39 14 25 43 3 3 22 21 1 34 3 3 35 19 16 73 3 3 49 7 42 31 2 3 48 18 30 34 2 3 44 19 25 20 2 3 35 12 23 22 2 3 43 11 32 35 2 3 39 22 17 36 1 3 34 25 9 23 1 3 13 16 -3 21 1 3 73 13 60 17 1 3 25 11 14 27 1 3 27 13 14 15 1 3 10 1 3