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8.2 #40,42

40. The article "Selection of a Method to Determine Residual Chlorine in Sewage Effluents" (Water and Sewage Works, 1971: 360-364) reported the results of an experiment in which two different methods of determining chlorine content were used on samples of Cl 2 -demand-free water for various doses and contact times. Observations are in mg/L. Sample 1 2 3 4 MSI method .39 .84 1.76 3.35 SIB method .36 1.35 2.56 3.92 5 6 7 8 MSI method 4.69 7.70 10.52 10.92 SIB method 5.35 8.33 10.70 10.91 Does the true average content measured by one method appear to differ from that measured by the other method? State and test the appropriate hypotheses. Does the conclusion depend on whether a significance level of .05, .01, or .001 is used?

The article "Supervised Exercise Versus NonSupervised Exercise for Reducing Weight in Obese Adults" (J. Sport. Med. Phys. Fit., 2009: 85-90) reported on an investigation in which participants were randomly assigned either to a supervised exercise program or a control group. Those in the control group were told only that they should take measures to lose weight. After 4 months, the sample mean decrease in body fat for the 17 individuals in the experimental group was 6.2 kg with a sample standard deviation of 4.5 kg, whereas the sample mean and standard deviation for the 17 people in the control group were 1.7 kg and 3.1 kg, respectively. Assume normality of the two body fat loss distributions (as did the investigators). Does it appear that true average decrease in body fat is more than 2 kg larger for the experimental condition than for the control condition? Carry out a test of appropriate hypotheses using a significance level of .01.