Stat 301 B – Fall 2014 – Midterm exam 1
Information and JMP output
1. The histogram and box plot below show the concentration of Dioxin (in parts-per-trillion, ppt) in the
blood of 49 randomly chosen workers at a New Jersey chemical plant. The summary statistics describe
the sample of 49 workers. These 49 workers are a simple random sample of the 1550 workers at the
plant.
Mean
Std Dev
N
Variance
Minimum
Maximum
407.80192
277.79706
49
77171.208
87.815531
1159.6213
1
2. Oatmeal has been touted as a natural way to reduce blood pressure. One study drew a random
sample of middle-aged men from the population of all middle-aged male patients in a regional health
practice. These men were asked how much oatmeal they ate. The results below compare the group of
men who ate oatmeal 3 times a week (20 men) to the group who never ate oatmeal (42 men). They are
derived from JMP Fit Y by X, with Y = blood pressure (bp) and X = group.
t Test
hate-eat
Assuming equal variances
Difference
Std Err Dif
Upper CL Dif
Lower CL Dif
Confidence
9.1464
3.8924
16.9323
1.3605
0.95
t Ratio
2.34983
Means for Oneway Anova
Level
Number
Mean
Std Error
eat
20
117.067
3.2036
hate
42
126.213
2.2107
Std Error uses a pooled estimate of error variance
Means and Std Deviations
Level
Number Mean
eat
20
117.067
hate
42
126.213
Std Dev
13.5704
14.6645
Lower 95%
110.66
121.79
Upper 95%
123.48
130.64
Std Err Mean Lower 95% Upper 95%
3.0344
110.72
123.42
2.2628
121.64
130.78
2
3. The pesticide DDT was banned in part because it led to severe thinning of eggshells of many birds.
Since then, the effects of many pollutants on eggshell thickness have been measured. The following
analysis came from a study on the effects of PCB, polychlorinated biphenyl, in eggs of brown pelicans on
Anacapa Island, an island off the coast of southern California.
The investigators collected 65 eggs from brown pelican nests. Assume they were careful to collect only
one egg from each nest. In each egg, they measured the thickness of the egg shell, measured in
1000’ths of mm, and the concentration of PCB in the yolk, measured in parts per billion, ppb. The JMP
output from a Fit Y by X analysis, using Y = thickness and X=PCB concentration is below. Below the JMP
output is a portion of the data table with information for selected values of PCB concentration.
Linear Fit
thickness = 51.068738 - 0.0150253*PCB concentration (ppb)
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.014928
-0.00071
15.03459
47.74655
65
Parameter Estimates
Term
Intercept
PCB concentration
Estimate Std Error
51.068
3.877
-0.0150
0.0153
t Ratio Prob>|t| Lower 95% Upper 95%
13.17
<.0001 43.319
58.818
-0.98
0.3323 -0.0458
0.0157
3
Diagnostics Plots
Residual by Predicted Plot
Residual by Row Plot
Residual Normal Quantile Plot
PCB concentration
150
200
250
300
350
Predicted
48.8149384
48.0636718
47.3124053
46.5611387
45.8098722
Lower 95%
Mean thick
44.4950512
44.2811264
43.48156
42.1153992
40.3715521
4
Upper 95%
Mean thick
53.13482549
51.84621727
51.14325049
51.00687824
51.24819216
Lower 95%
Indiv thick
18.46173792
17.78227483
17.02493709
16.18977139
15.2774193
Upper 95%
Indiv thick
79.16813882
78.34506879
77.59987343
76.93250602
76.34232501
5