How large is the difference between the percentage of returns for successful and unsuc-

Env. 6.9 The study of concentrations of atmospheric trace metals in isolated areas of the world has received considerable attention because of the concern that humans might somehow alter the climate of the earth by changing the amount and distribution of trace metals in the atmosphere. Consider a study at the south pole, where at 10 different sampling periods throughout a 2-month period, 10,000 standard cubic meters scm of air were obtained and analyzed for metal concentrations. The results associated with magnesium and europium are listed here. Note: Magnesium results are in units of 10 ⫺ 9 gscm; europium results are in units of 10 ⫺ 15 gscm. Note that s ⬎ for the magnesium data. Would you expect the data to be normally distributed? Explain. Sample Size Sample Mean Sample Standard Deviation Magnesium 10 1.0 2.21 Europium 10 17.0 12.65 6.10 Refer to Exercise 6.9. Could we run a t test comparing the mean metal concentrations for magnesium and europium? Why or why not? Env. 6.11 PCBs have been in use since 1929, mainly in the electrical industry, but it was not until the 1960s that they were found to be a major environmental contaminant. In the paper “The ratio of DDE to PCB concentrations in Great Lakes herring gull eggs and its use in interpreting contam- inants data” [appearing in the Journal of Great Lakes Research 24 1: 12 –31, 1998], researchers report on the following study. Thirteen study sites from the five Great Lakes were selected. At each site, 9 to 13 herring gull eggs were collected randomly each year for several years. Following collection, the PCB content was determined. The mean PCB content at each site is reported in the following table for the years 1982 and 1996. Site Year 1 2 3 4 5 6 7 8 9 10 11 12 13 1982 61.48 64.47 45.50 59.70 58.81 75.86 71.57 38.06 30.51 39.70 29.78 66.89 63.93 1996 13.99 18.26 11.28 10.02 21.00 17.36 28.20 7.30 12.80 9.41 12.63 16.83 22.74

a. Legislation was passed in the 1970s restricting the production and use of PCBs. Thus,

the active input of PCBs from current local sources has been severely curtailed. Do the data provide evidence that there has been a significant decrease in the mean PCB content of herring gull eggs?

b. Estimate the size of the decrease in mean PCB content from 1982 to 1996, using a

95 confidence interval.

c. Evaluate the conditions necessary to validly test hypotheses and construct confidence

intervals using the collected data. d. Does the independence condition appear to be violated? y Two-Sample T-Test and Confidence Interval Two-sample T for No Newspaper vs Newspaper N Mean StDev SE Mean No Newspaper 30 32.0 16.0 2.9 Newspaper 25 40.91 7.48 1.5 95 CI for mu No Newspaper mu Newspaper: 15.5, 2.2 T-Test mu No Newspaper mu Newspaper vs : T 2.70 P 0.0049 DF 42 6.12 Refer to Exercise 6.11. There appears to be a large variation in the mean PCB content across the 13 sites. How could we reduce the effect of variation in PCB content due to site differ- ences on the evaluation of the difference in the mean PCB content between the two years? H.R. 6.13 A firm has a generous but rather complicated policy concerning end-of-year bonuses for its lower-level managerial personnel. The policy’s key factor is a subjective judgment of “contri- bution to corporate goals.” A personnel officer took samples of 24 female and 36 male managers to see whether there was any difference in bonuses, expressed as a percentage of yearly salary. The data are listed here: Gender Bonus Percentage F 9.2 7.7 11.9 6.2 9.0 8.4 6.9 7.6 7.4 8.0 9.9 6.7 8.4 9.3 9.1 8.7 9.2 9.1 8.4 9.6 7.7 9.0 9.0 8.4 M 10.4 8.9 11.7 12.0 8.7 9.4 9.8 9.0 9.2 9.7 9.1 8.8 7.9 9.9 10.0 10.1 9.0 11.4 8.7 9.6 9.2 9.7 8.9 9.2 9.4 9.7 8.9 9.3 10.4 11.9 9.0 12.0 9.6 9.2 9.9 9.0

a. Identify the value of the pooled-variance t statistic the usual t test based on the equal

variance assumption. b. Identify the value of the t⬘ statistic. c. Use both statistics to test the research hypothesis of unequal means at a ⫽ .05 and at a ⫽ .01. Does the conclusion depend on which statistic is used? Boxplots of females’ and males’ bonuses means are indicated by solid circles Males’ bonuses Females’ bonuses 6 7 8 9 10 11 12 Bonus percentage Two-Sample T-Test and Confidence Interval Two-sample T for Female vs Male N Mean StDev SE Mean Female 24 8 .53 1.19 0.24 Male 36 9.68 1.00 0.17 95 CI for mu Female mu Male: 1.74, 0.56 T-Test mu Female mu Male vs : T 3.90 P 0.0002 DF 43 95 CI for mu Female mu Male: 1.72, 0.58 T-Test mu Female mu Male vs : T 4.04 P 0.0001 DF 58 Both use Pooled StDev 1.08