The table below shows a record of the "before" and "after" weights (in pounds) of 20 patients enrolled in a clinically-supervised ten-week weight-loss program.
|
Patient #
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
Before Wt (lbs)
|
272
|
319
|
253
|
325
|
236
|
233
|
300
|
260
|
268
|
276
|
|
After Wt (lbs)
|
263
|
313
|
251
|
312
|
227
|
227
|
290
|
251
|
262
|
263
|
|
Patient #
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
|
Before Wt (lbs)
|
215
|
245
|
248
|
364
|
301
|
203
|
197
|
217
|
210
|
223
|
|
After Wt (lbs)
|
206
|
235
|
237
|
350
|
288
|
195
|
193
|
216
|
202
|
214
|
Let XB represent the "Before" weight and XA the "After" weight.
(i) Using the same bin size for each data set, obtain histograms for the XB and XA data and plot both on the same graph. Strictly on the basis of a visual inspection of these histograms, what can you say about the effectiveness of the weight-loss program in achieving its objective of assisting patients to lose weight?
(ii) De?ne the difference variable, D = XB - XA , and from the given data, obtain and plot a histogram for this variable. Again, strictly from a visual inspection of this histogram, what can you say about the effectiveness of the weight-loss program?