Researchers conducted a study to determine which of two treatments, A or B, is more effective in the treatment of kidney stones. The results of their experiment are given in the table.

(a) Which treatment appears to be more effective? Why? The data in the table above do not take into account the size of the kidney stone. The data shown next indicate the effectiveness of each treatment for both large and small kidney stones.

(b) Determine the proportion of small kidney stones that were effectively dealt with using treatment A. Determine the proportion of small kidney stones that were effectively dealt
with using treatment B.
(c) Repeat part (b) for the large stones to create a conditional distribution of effectiveness by treatment for each stone size.
(d) Draw a bar graph of the conditional distribution from part (c).
(e) Write a short report detailing your findings.

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Total 562 138 700 Treatment ATreatment B Effective Not effective Total 273 289 61 350 350 Small Stones Large Stones 234 273 36 Effective 81 Not effective 25