EPOM405 Homework Assignment M9
1. Use the following methods to test Ho: μ₁ = μ2 versus H₁ μ₁ ± μ2 for the data in worksheet 9.1 of
the Excel data file:
a. Tukey's Quick Test
b. A boxplot slippage test
c. The two-sample t test
d. The Mann-Whitney test (use Stat> Nonparametrics> Mann-Whitney)
2. Use the following methods to test H0 µ₁ = μ2 versus H₁ : µ₁ ± µ2 for the data in worksheet 9.2 of
the Excel data file:
a. Tukey's Quick Test
b. A boxplot slippage test
c. The two-sample t test
d. The Mann-Whitney test
3. Use the data from worksheet 9.2 to test for a difference between the two population standard
deviations:
a. By manually calculating the F statistic and comparing it to the F0.95 critical value.
b. By calculating the p value for the F statistic (Cal> Probability Distributions or Graph>
Probability Distribution Plot) and comparing it to a = = 0.05.
c. Using the F statistic in MINITAB via Stat> Basic Statistics> 2 Variances> Options> Use Test
and Confidence Intervals Based on Normal Distributions.
d. Using Bonnet's and Levene's tests in MINITAB by turning off the normality assumption option
in part c.
e. Compare the results of the F, Bonnet's, and Levene's methods. Do they agree? What if they
don't?
4. Determine the 95% confidence interval for the true process cp if a sample of size n =
S = 0.0042 and the spec is USL/LSL = 1.500 ± 0.020.
80 gives
5. An experiment was performed to study the defective rate of a process. The hypotheses to be tested
were Ho : p 0.01 vs. H₁ : p > 0.01. A sample of size n = 100 parts was drawn, inspected, and
=
found to have D =
3 defectives. (Hint: Use Stat> Basic Statistics> 1 Proportion.)
a. Is there sufficient evidence to reject Ho?
b. What is the one-sided upper 95% confidence limit for p?
6. In an experiment to compare the incidence of heart disease in populations eating the Mediterranean
diet vs. a western diet 14 of 219 people from the Mediterranean diet group had heart attacks and 44 of
204 people from the western diet group had heart attacks.
a. Use Fisher's Exact Test and the large sample (i.e. normal approximation to the binomial
distribution) test to determine if there is a difference in the heart attack rates. (Hint: Use Stat>
Basic Statistics> 2 Proportions.)
b. Use the x² test for association to determine if there is a difference in the heart attack rates. (Hint:
Use Stat> Basic Statistics> Tables> Cross Tabulation and Chi-square or > Chi-square Test
for Association.)
c. Do the three methods agree? When will the Fisher's method be preferred and the other two
methods avoided?
MM&B Inc. 7. Precision valves for controlling the flow of fluids and liquids can be assembled in a clean room or on
a less-clean production line. The cleanliness of the assembly process can affect the leak rate. Twenty
valve assemblies were made on the production line and another twenty were made in the clean room.
The same component lots were used for all forty assemblies.
a. There were three leakers from the production line versus zero leakers from the clean room. Is
there sufficient evidence to conclude that the leak rate on the production line is worse than the
leak rate in the clean room?
b. What's the smallest number of defectives that would have to be found on the production line with
no defectives found in the clean room to conclude that the production line leaker rate is worse
that in the clean room?
8. Cheap plastic children's dice are made by pressing divots in the die faces causing the dice to be
unbalanced, e.g. the side with a 6 will be light and the side with a 1 will be heavy. To test this claim,
dice were rolled 180 times and the observed frequencies of 1-6 were found to be 30, 32, 22, 34, 39,
23. (The data are in worksheet 9.8.) Test the observed frequencies to see if they are consistent with the
null hypothesis Ho: The dice are balanced versus HA: The dice are unbalanced by:
a. Manual calculate the x² statistic and compare it to the appropriate critical value.
b. Confirm your answer to part a using MINITAB Stat> Tables> Chi-square Goodness of Fit Test
(One Variable).
MM&B Inc. EPOM405 Homework Assignment M9 Answers to Selected Questions
1. a) (T = 6) < (T0.05 = 7) so cannot reject Ho
b) boxes are overlapped, cannot reject Ho
c) t = −2.16, p
=
0.059 so cannot reject Ho at a
0.05
d) (p = 0.071) > (α = 0.05) so cannot reject Ho
2. a) T
=
7 so reject Ho
b) sample sizes are large and one median is slipped from the other sample's box so reject Ho
c) t = -2.78, p = 0.008 so reject Ho at a
=
0.05
d) p = 0.0023 so reject Ho at a
=
0.05
3.
a. (F = 2.72) > (F0.95
=
1.76) so reject Ho and conclude that the variances are not equal
b. One-tailed test, (p = 0.0019) < (α = 0.05) so reject Ho and conclude that the variances are not
equal
c. MINITAB's F
two-tailed test
d. PBonnet
=
=
0.37 is the reciprocal of F = 2.72 and its p
=
0.004 value is for its default
=
0.023, both two-tailed tests
0.008 and p Levine
e. All of the methods agree
4. P(1.38 < Cp < 1.80) = 0.95
5.
a. p
0.079
b. LCL = 0.0082
6.
a. pFisher
=
0.000, z = -4.57, p = 0
7.
b. x² 20.6 with df = 1, p = 0
a. p = 0.115
b. 5
8. x² = 7.13, p = 0.211
MM&B Inc.
