Pollen Removal. As part of a study to investigate reproductive strategies in plants, biologists recorded the time spent at sources of pollen and the proportions of pollen removed by bumblebee queens and honeybee workers pollinating a species of lily. (Data from L. D. Harder and J. D. Thompson, "Evolutionary Options for Maximizing Pollen Dispersal of Animal-pollinated Plants," American Naturalist 133 (1989): 323-44.) Their data appear in Display 3.12.

(a) (i) Draw side-by-side box plots (or histograms) of the proportion of pollen removed by queens and workers. (ii) When the measurement is the proportion P of some amount, one useful transformation is logOEP=.1 ! P/". This is the log of the ratio of the proportion removed to the proportion not removed. Draw side-by-side box plots or histograms on this transformed scale. (iii) Test whether the distribution of proportions removed is the same or different for the two groups, using the t -test on the transformed data.

(b) Draw side-by-side box plots of duration of visit on (i) the natural scale, (ii) the logarithmic scale, and (iii) the reciprocal scale. (iv) Which of the three scales seems most appropriate for use of the t -tools? (v) Compute a 95% confidence interval to describe the difference in means on the chosen scale. (vi) What are relative advantages of the three scales as far as interpretation goes? (vii) Based on your experience with this problem, comment on the difficulty in assessing equality of population standard deviations from small samples.