18.02.2022
IE6103 DESIGN OF EXPERIMENTS
PRACTICE 1
1. CONFIDENCE INTERVAL ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE KNOWN
The life in hours of a 75-watt light bulb is known to be normally distributed with . A
random sample of 20 bulbs has a mean life of .
(a)
Construct a 95% two
-
sided confidence interval on the mean life.
(b)
Construct a 95% lower
-
confidence bound on the mean life. Compare the lower bound of this
confidence interval with the one in part a.
2. STATISTICAL INTERVALS FOR A SINGLE SAMPLE
A machine produces metal rods used in an automobile suspension system. A random sample of 15
rods is selected, and the diameter is measured. The resulting data (in millimeters) are as follows:
8.24
8.25
8.20
8.23
8.24
8.21
8.26
8.26
8.20
8.25
8.23
8.23
8.19
8.28
8.24
(a)
Calculate a 95% two
-
sided confidence interval on mean rod diameter.
(b)
Calculate a 95% upper confidence bound on the mean. Compare this bound with the upper
bound of the two-sided confidence interval and discuss why they are different.
3. TESTS ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE KNOWN
A bearing used in an automotive application is supposed to have a nominal inside diameter of 1.5
inches. A random sample of 25 bearings is selected, and the average inside diameter of these
bearings is 1.4975 inches. Bearing diameter is known to be normally distributed with standard
deviation . Test the hypothesis versus using .
4. (Extra)
Medical researchers have developed a new artificial heart constructed primarily of titanium and
plastic. The heart will last and operate almost indefinitely once it is implanted in the patient’s body,
but the battery pack needs to be recharged about every four hours. A random sample of 50 battery
packs is selected and subjected to a life test. The average life of these batteries is 4.05 hours. Assume
that battery life is normally distributed with standard deviation 0.2 hour.
(a) Is there evidence to support the claim that mean battery life exceeds 4 hours? Is the alternative
hypothesis one- or two-sided? Use alpha=0.05.
(b) Explain how the question in part (a) could be answered by constructing a one-sided confidence
bound on the mean life.
5. TESTS ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE UNKNOWN
A research journal is reported body temperature, gender, and heart rate for a number of subjects.
The body temperatures for 25 female subjects follow:
97.8, 97.2, 97.4, 97.6, 97.8, 97.9, 98.0, 98.0, 98.0, 98.1, 98.2, 98.3, 98.3, 98.4, 98.4, 98.4, 98.5, 98.6,
98.6, 98.7, 98.8, 98.8, 98.9, 98.9, and 99.0.
(a) Test the hypotheses versus using . Find the P-value.
(b) Explain how the question in part (a) could be answered by constructing a two-sided confidence
interval on the mean female body temperature.
