In given Problem data are presented on counts of bacteria on 12 plates by two observers. Both observers counted the same plate and their counts were recorded. In Problem, a confidence interval was computed on the difference in the mean counts. The confidence limits did not include 0.
(a) Plot a scatter diagram of this data and compute r.
(b) Contrast what you can learn from a scatter plot and T with what you can learn from a confidence limit about the differences in the means.
Problem
Bacterial colonies were counted on 12 plates. There were two observers, and the plate counts obtained were as follows:
|
Plate Number
|
Observer 1
|
Observer 2
|
Observer 3
|
|
1
|
139
|
191
|
-52
|
|
2
|
121
|
181
|
-60
|
|
3
|
49
|
67
|
-18
|
|
4
|
163
|
143
|
20
|
|
5
|
191
|
234
|
-43
|
|
6
|
61
|
80
|
-19
|
|
7
|
179
|
250
|
-71
|
|
8
|
218
|
239
|
-21
|
|
9
|
297
|
289
|
8
|
|
10
|
165
|
201
|
-36
|
|
11
|
91
|
80
|
11
|
|
12
|
92
|
99
|
-7
|
Give a 99% confidence interval for the difference between the mean plate counts of the two observers. Do you believe that there is a difference? Why?