Do the data provide sufficient evidence that rats exposed to a 5°C environment have a

26°C 5°C Rat Blood Pressure Rat Blood Pressure 1 152 7 384 2 157 8 369 3 179 9 354 4 182 10 375 5 176 11 366 6 149 12 423 Env. 6.6 A pollution-control inspector suspected that a riverside community was releasing semi- treated sewage into a river and this, as a consequence, was changing the level of dissolved oxygen of the river. To check this, he drew 15 randomly selected specimens of river water at a location above the town and another 15 specimens below. The dissolved oxygen readings, in parts per mil- lion, are given in the accompanying table. Above Town 5.2 4.8 5.1 5.0 4.9 4.8 5.0 4.7 4.7 5.0 4.7 5.1 5.0 4.9 4.9 Below Town 4.2 4.4 4.7 4.9 4.6

4.8 4.9

4.6 5.1 4.3 5.5 4.7 4.9 4.8 4.7 Use the computer output shown here to answer the following questions. a. Do the data provide sufficient evidence to indicate a difference in mean oxygen content between locations above and below the town? Use a ⫽ .05. b. Was the pooled t test or the separate-variance t test used in the computer output? c. Do the required conditions to use the test in a appear to be valid for this study? Justify your answer. d. How large is the difference between the mean oxygen content above and below the town? Engin. 6.7 An industrial engineer conjectures that a major difference between successful and unsuccess- ful companies is the percentage of their manufactured products returned because of defectives. In a study to evaluate this conjecture, the engineer surveyed the quality control departments of 50 suc- cessful companies identified by the annual profit statement and 50 unsuccessful companies. The companies in the study all produced products of a similar nature and cost. The percentage of the total output returned by customers in the previous year is summarized in the following graphs and tables. Boxplots of above- and below-town specimens means are indicated by solid circles 5.5 5.0 4.5 4.0 Above-town specimens Below-town specimens Dissolved oxygen content Two-Sample T-Test and Confidence Interval Two-sample T for Above Town vs Below Town N Mean StDev SE Mean Ab ove To 15 4.92 0.157 0.042 Below To 15 4.74 0.320 0.084 95 CI for mu Above To mu Below To: 0.013, 0.378 T-Test mu Above To mu Below To vs not : T 1.95 P 0.065 DF 20

a. Do the data provide sufficient evidence that successful companies have a lower percent-

age of their products returned by customers? Use a ⫽ .05. b. Was the pooled t test or the separate-variance t test used in the computer output? c. Do the required conditions to use the test in a appear to be valid for this study? Justify your answer.

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

cessful companies? Soc. 6.8 The number of households currently receiving a daily newspaper has decreased over the last 10 years, and many people state they obtain information about current events through television news and the Internet. To test whether people who receive a daily newspaper have a greater knowl- edge of current events than people who don’t, a sociologist gave a current events test to 25 randomly selected people who subscribe to a daily newspaper and to 30 randomly selected persons who do not receive a daily newspaper. The following stem-and-leaf graphs give the scores for the two groups. Does it appear that people who receive a daily newspaper have a greater knowledge of cur- rent events? Be sure to evaluate all necessary conditions for your procedures to be valid. Character Stem-and-Leaf Display Stem-and-leaf of No Newspaper Deliver Stem-and-leaf of Newspaper Subscribers N N 3 25 Lea f Unit t i n U f a e L . 1 1.0 0 000 1 3 1 59 2 2 4 3 3 2 9 9 2 7 5 2 2 3 4 3 2 3 9 8 8 6 6 3 9 8 5 5 3 3 3 3 2 1 1 4 4 2 1 4 6 6 6 5 5 4 5 4 2 5 5 9 5 5 5 5 6 2 Boxplots of unsuccessful and successful businesses means are indicated by solid circles 15 10 5 Unsuccessful businesses Successful businesses Percentage of defectives Two-Sample T-Test and Confidence Interval Two-sample T for Unsuccessful vs Successful N Mean StDev Se Mean Unsuccessful 50 9.08 1.97 0.28 Successful 50 5.40 2.88 0.41 95 CI for mu Unsuccessful mu Successful: 2.70, 4.66 T-Test mu Unsuccessful mu Successful vs : T 7.46 P 0.0000 DF 86 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