STATISTICS 401B
Spring 2016
Laboratory Assignment 6
1. PCBs have been in use since 1929, mainly in the electrical industry, but it was not until the 1960s that they
were found to be a major environmental contaminant. In 1998, researchers reported the following study in
an environmental journal: Thirteen study sites from the five Great Lakes were selected. At each site, 9 to
13 herring gull eggs were randomly collected each year for several years an the mean PCB content in the
eggs were determined. The following are data for the years 1982 and 1996:
Site
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
1982 61.48 64.47 45.50 59.70 58.81 75.86 71.57 38.06 30.51 39.70 29.78 66.89 63.93
1996 13.99 18.26 11.28 10.02 21.00 17.36 28.20
7.30 12.80
9.41 12.63 16.83 22.74
Note: Do all computations for parts (b),(c), and (d) using hand calculation. Use Excel to compute
P
P
di , d2i , i = 1, . . . , 13 and thus
di , d2i and sd and sd¯. Use the output from a JMP analysis using the
data file gull egg PCB.jmp downloaded from the web page to provide answers to parts (a),(e) and (f).
Turn in the Excel page and marked JMP output page and show work.
(a) Do the Normal probability plot and the boxplot from the JMP output indicate whether it is valid to
use a paired t-test? Explain.
(b) Legislation was passed in the 1970s restricting production and use of PCBs. Thus the active infusion
of PCBs from local sources has been severely curtailed. Compute the paired t-statistic to test the
research hypotheses that there has been a significant decrease in mean PCB content in herring gull
eggs. Use α = .01. State your hypotheses clearly. Define the symbols you use carefully.
(c) Explain what is meant by the p-value in words by defining it for the above test. Show how to find
bounds for the p-value of the above test using the t-table.
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(d) Use a 98% confidence interval to estimate the decrease in the mean PCB content in herring gull eggs.
Test the hypothesis in part (b) using this interval stating the α level used for this test clearly. State
your conclusion.
(e) Extract the t-statistic from the JMP output for testing the hypothesis you stated in part (b). Circle
it in the JMP output. State the p-value associated with this test extracted from the JMP output.
(f) Extract the 98% confidence interval for the decrease in the mean PCB content in herring gull eggs
from the JMP output. Copy it here and circle it in the JMP output.
2. Twenty observations on etch uniformity on silicon wafers, y, are taken during a qualification experiment
for a plasma etcher. The data are: 5.34, 6.00, 5.97, 5.25, 6.65, 7.55, 7.35, 6.35, 4.76, 5.54, 5.44, 4.61, 5.98,
5.62, 4.39, 6.00, 7.25, 6.21, 4.98, 5.32. Use this data to provide answers to the following questions.
P
Note: Do all computations for parts (b), and (c), using hand calculation. For this data
y = 116.56,
P 2
y = 694.33. Use the output from a JMP analysis to provide answers to parts (a),(d) and (e). Turn in
the marked JMP output and show work.
(a) Do the box plot or the normal probability plot indicate any violation of the conditions underlying the
use of the chi-square procedures for constructing confidence intervals or testing hypotheses about σ?
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(b) A quality control inspector might require the etch uniformity of the wafers to be reasonably consistent, in particular, that σ of more than 1 unit to be unsatisfactory. Is there sufficient evidence in the
data to determine that the standard deviation meets this criterion? State appropriate hypotheses and
perform a test with α = .05.
(c) Estimate the standard deviation of the etch uniformity of the wafers using a 95% confidence interval.
(d) Extract the statistic from the JMP output for testing the hypothesis you stated in part (b). Circle it
in the JMP output. State the p-value associated with this test extracted from the JMP output.
(e) Extract the 95% confidence interval for the standard deviation of the etch uniformity of the wafers
from the JMP output. Copy it here and circle it in the JMP output.
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3. An investigation was conducted into the dust content in the flue gases of two types of solid-fuel boilers.
Thirteen boilers of type A and nine boilers of type B were used under different fuels (coal, wood, straw,
etc.) at various temperature settings. Over a period of time, following quantities of dust, in grams, were deposited in similar dust traps inserted in each of the 22 flues. The data (also available in boiler dust.jmp)
are given below:
Boiler
type A
type B
72.1
51.0
58.4
39.3
82.1
52.8
67.2
58.8
Dust Content (in grams)
76.7 75.1 48.0 53.3 55.5
41.2 66.6 46.0 56.4 58.9
P
61.5
60.6
55.2
63.1
y
828.8
471.0
y2
54096.52
25289.94
P
(a) Use the normal probability plot and the boxplots output from the JMP output to comment on whether
the assumption of normality of the two populations is reasonable. Does these plots support the assumption that the population variances are the same for the two populations? Explain
(b) Compute the sample variances s2A and s2B , respectively, of the two samples using the above summary
statistics. (Must use hand computation)
(c) Compute a statistic to test the research hypothesis that the two population variances of the dust
content distributions are different using α = .05 by hand. State your hypotheses, the rejection region
and your conclusion. (Must use hand computation)
(d) Extract the statistic from the JMP analysis for testing the hypothesis you stated in part (b). Circle
it in the JMP output. State the p-value associated with this test extracted from the JMP output.
Due Tuesday, March 22, 2016 (turn-in during lab)
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