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```EQC7016
Statistical Methods for Quality Management
Week 2 Exercises
Sem 1 2020/2021
Statistical Quality Control – A Modern Introduction (7th Ed), International Edition;
Douglas Montgomery
Chapter 3
3.3.
The content of liquid detergent bottles is being analyzed. Twelve bottles,
randomly selected from the process, are measured, and the results are as
follows (in fluid ounces):
16.05, 16.03, 16.02, 16.04, 16.05, 16.01, 16.02, 16.02, 16.03, 16.01, 16.00,
16.07
a) Calculate the sample average.
b) Calculate the sample standard deviation
3.4.
The service time in minutes from admit to discharge for ten patients seeking
care in a hospital emergency department are 21, 136, 185, 156, 3, 16, 48, 28,
100, and 12. Calculate the mean and standard deviation of the service time.
3.5.
The Really Cool Clothing Company sells its products through a telephone
ordering process. Since business is good, the company is interested in
studying the way that sales agents interact with their customers. Calls are
randomly selected and recorded, then reviewed with the sales agent to
identify ways that better service could possibly be provided or that the
customer could be directed to other items similar to those they plan to
purchase that they might also find attractive. Call handling time (length) in
minutes for 20 randomly selected customer calls handled by the same sales
agent are as follows:
5, 26, 8, 2, 5, 3, 11, 14, 4, 5, 2, 17, 9, 8, 9, 5, 3, 28, 22, and 4. Calculate the
mean and standard deviation of call handling time.
Chapter 4
4.7.
The inside diameters of bearings used in an aircraft landing gear assembly
are known to have a standard deviation of 0.002 cm. A random sample of 15
bearings has an average inside diameter of 8.2535 cm.
(a) Test the hypothesis that the mean inside bearing diameter is 8.25 cm. Use
a two sided alternative and α = 0.05 (b) Find the P-value for this test.
(c) Construct a 95% two-sided confidence interval on the mean bearing
diameter.
4.10. Using the data from Exercise 4.7, construct a 95% lower confidence interval on
mean battery life. Why would the manufacturer be interested in a onesided
confidence interval?
4.8.
The tensile strength of a fiber used in manufacturing cloth is of interest to the
purchaser. Previous experience indicates that the standard deviation of
tensile strength is 2 psi. A random sample of eight fiber specimens is
selected, and the average tensile strength is found to be 127 psi.
(a) Test the hypothesis that the mean tensile strength equals 125 psi versus
the alternative that the mean exceeds 125 psi. Use α = 0.05.
(b) What is the P-value for this test?
(c) Discuss why a one-sided alternative was chosen in part (a).
(d) Construct a 95% lower confidence interval on the mean tensile strength.
4.9.
The service life of a battery used in a cardiac pacemaker is assumed to be
normally distributed. A random sample of ten batteries is subjected to an
accelerated life test by running them continuously at an elevated temperature
until failure, and the following lifetimes (in hours) are obtained:
25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.
(a) The manufacturer wants to be certain that the mean battery life exceeds
25
h. What conclusions can be draw
(b) Construct a 90% two-sided confidence interval on mean life in the
accelerated test.
4.12. A machine is used to fill containers with a liquid product. Fill volume can be
assumed to be normally distributed. A random sample of ten containers is
selected, and the net contents (oz) are as follows:
12.03, 12.01, 12.04, 12.02, 12.06, 11.98, 11.97, 12.02, 12.05, and 11.99.
(a) Suppose that the manufacturer wants to be sure that the mean net contents
exceeds 12 oz. What conclusions can be drawn from the data (use α = 0.01).
(b) Construct a 99% two-sided confidence interval on the mean fill volume.
4.16. Two machines are used for filling glass bottles with a soft-drink beverage. The
filling have known standard deviation of 1 = 0.010 liter and 2= 0.005 liter
processes respectively. A random sample of n1 = 25 bottles from machine 1
and n2 = 15 bottles from machine 2 results in average net contents of 1 x =
2.03 liters and 2 x = 2.07 liters.
(a) Test the hypothesis that both machines fill to the same net contents, using
α = 0.05. What are your conclusions?
(b) Find the P-value for this test.
(c) Construct a 95% confidence interval on the difference in mean fill volume.
4.17. Two quality control technicians measured the surface finish of a metal part,
obtaining the data in Table 4E.1(Refer to Data File) Assume that the
measurements are normally distributed.
a) Test the hypothesis that the mean surface finish measurements made by
the two technicians are equal. Use α = 0.05 and assume equal variances.
b) What are the practical implications of the test in part (a)? Discuss what
practical conclusions you would draw if the null hypothesis were rejected.
c) Assuming that the variances are equal, construct a 95% confidence
interval on the mean difference in surface-finish measurements.
d) Test the hypothesis that the variances of the measurements made by the
two technicians are equal. What are the practical implications if the null
hypothesis is rejected?
```