Reference no: EM131110021

In 1997, scientists at the Horticulture Research International-East Manning conducted an exploratory study to assess the potential impact of RSS. The results of this investigation were reported in Murray, Ridout, and Cross (2000). A portion of the study focused on a comparison of spray deposit coverage on tree leaves under two different sprayer configurations. Two similar plots of apple trees were sprayed with a fluorescent, water-soluble tracer Tinopal CBS-X at 2% concentration in water. One of the plots was sprayed at high volume with a coarse nozzle on the sprayer (coarse treatment) to provide large average droplet size. The second plot was sprayed at low volume with a fine nozzle on the sprayer (fine treatment) to provide small average droplet size. The investigators were interested in both the percentage of upper leaf surface covered by the spray and the total amount of spray deposited on the upper surfaces of the leaves. In this problem, we concentrate solely on the percentage of upper leaf surface covered by the spray and denote this variable by %Coverage (expressed as a decimal).

With the RSS methodology in mind, 25 sets of five leaves each (common set size k = q = 5) were collected from the central trees of each of these two plots. Leaves of similar size were selected throughout the tree canopies, with care to avoid any intentional bias, but without any formal randomization scheme. For our purposes in this problem, we will view these 250 collected leaves as 50 independent random samples (25 from each plot) of size 5 each.

The leaves were taken to the laboratory where a scientist ranked (without formal measurement) the %Coverage on the upper surfaces of each of the leaves within these 100 sets of five leaves based on visual appearance of the deposits on the upper leaf surfaces when viewed under ultraviolet light. Once these visual rankings were completed, the image analysis system Optimax V was used to formally estimate the percentage areas of the individual upper leaf surfaces that were covered with deposit.

The scientist's within-set rankings and the Optimax V estimated %Coverage data from this experiment are presented in Table 15.7. With common set size k = q = 5, randomly select five of the 25 sets of rankings for the coarse treatment data on which to utilize the Optimax V measurement for the smallest ranked leaf in each of the five sets. Then randomly select a second set of five of the remaining 20 sets of rankings for the coarse treatment data on which to utilize the Optimax V measurement for the second smallest ranked leaf in each of the five sets. Continue in this fashion through a third randomly selected set of five (from among the 15 remaining sets) where the Optimax V measurement for the third smallest ranked leaf is utilized, then a fourth randomly selected set of five (from among the 10 remaining sets) where the Optimax V measurement for the fourth smallest ranked leaf is utilized. Finally, the Optimax V measurement for the largest ranked leaf will be utilized from the remaining five sets. This yields an RSS of size m = c(k) = 5(5) = 25 from the coarse treatment data. We proceed in a similar fashion to obtain an independent RSS of size n = d(q) = 5(5) = 25 from the fine treatment data.

Find the P-value for the BW test of the conjecture that the upper leaf surface %Coverage is higher for the coarse treatment than for the fine treatment.