If vegetables intended for human consumption contain any pesticides at all, these pesticides should occur in minute quantities. Detection of pesticides in vegetables sent to market is accomplished by using solvents to extract the pesticides from the vegetables and then performing tests on this extract to isolate and quantify the pesticides present. The extraction process is thought to be adequate because, if known amounts of pesticides are added to "clean" vegetables in a laboratory environment, essentially all the pesticide can be recovered from the artificially contaminated extract.
The following data were obtained from a study by Willis Wheeler and colleagues, $^{\star}$ who sought to determine whether the extraction process is also effective when used in the more realistic situation where pesticides are applied to vegetable crops. Dieldrin (a commonly used pesticide) labeled with (radioactive) carbon-14 was applied to growing radishes. Fourteen days later, the extraction process was used, and the extracts were analyzed for pesticide content. A liquid scintillation counter was used to determine the amount of carbon-14 present in the extract and also the amount left behind in the vegetable pulp. Because the vegetable pulp typically is discarded when analyzing for pesticides, if an appreciable proportion of pesticide remains in this pulp, a serious underassessment of the amount of pesticide could result. The pesticide was the only source of carbon-14; thus, the proportion of carbon-14 in the pulp is likely to be indicative of the proportion of pesticide in the pulp. The following table shows a portion of the data that the researchers obtained when low, medium, and high concentrations of the solvent, acetonitrile, were used in the
extraction process.
a. Is there sufficient evidence that the mean percentage of carbon-14 remaining in the vegetable pulp differs for the different concentrations of acetonitrile used in the extraction process? Give bounds for, or use the appropriate applet to determine the attained significance level. What would you conclude at the $\alpha=.01$ level of significance?
b. What assumptions are necessary to validly employ the analysis that you performed in part (a)? Relate the necessary assumptions to the specific application represented in this exercise.
The Analysis of Variance
An Analysis of Variance Table for a…