Refer to Exercise 6.60. Suppose we wish to test the research hypothesis that m

Boxplots of placebo and progabide means are indicated by solid circles Placebo Progabide

10 20

30 40 50 60 Number of seizures Boxplots of midsize and SUV damage amounts means are indicated by solid circles Midsize SUV 30 20 10 Damage amounts in hundreds of dollars

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

seizures for epileptics? Use both a t test and the Wilcoxon test with a ⫽ .05. b. Which test appears to be most appropriate for this study? Why? c. Estimate the size of the differences in the mean number of seizures between the two groups. Bus. 6.64 Many people purchase sports utility vehicles SUVs because they think they are sturdier and hence safer than regular cars. However, preliminary data have indicated that the costs for re- pairs of SUVs are higher than for midsize cars when both vehicles are in an accident. A random sample of 8 new SUVs and 8 midsize cars are tested for front impact resistance. The amounts of damage in hundreds of dollars to the vehicles when crashed at 20 mph head on into a stationary barrier are recorded in the following table. Car 1 2 3 4 5 6 7 8 SUV 14.23 12.47 14.00 13.17 27.48 12.42 32.59 12.98 Midsize 11.97 11.42 13.27 9.87 10.12 10.36 12.65 25.23 a. Plot the data to determine whether the conditions required for the t procedures are valid. b. Do the data support the conjecture that the mean damage is greater for SUVs than for midsize vehicles? Use a ⫽ .05 with both the t test and Wilcoxon test. c. Which test appears to be the more appropriate procedure for this data set? d. Do you reach the same conclusions from both procedures? Why or why not? Two-Sample T-Test and Confidence Interval Two-sample T for Midsize vs SUV N Mean StDev SE Mean Midsize 8 13.11 5.05 1.8 SUV 8 17.42 7.93 2.8 95 CI for mu Midsize mu SUV: 11.4, 2.8 T-Test mu Midsize mu SUV vs : T 1.30 P 0.11 DF 14 Both use Pooled StDev 6.65 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