Chi-Kong Ng, ENGG2780B, Dept.

of SEEM, CUHK 1:1

Chapter 1.

Introduction
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:2

1.1. Engineering Method and the Steps in

Engineering Method
1.1.1. Engineering Method
• An engineer is someone who solves problems of interest to society
by the efficient application of scientific principles.
• Engineers accomplish this by either refining an existing product
or process or by designing a new product or process that meets
customers’ needs.
• The engineering method is the approach to formulating and solving
these problems.
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:3

1.1.2. Eight Steps in Engineering Method

1. Develop a clear and concise description of the problem.
2. Identify, at least tentatively, the important factors that affect this
problem or that may play a role in its solution.
3. Propose a model for the problem, using scientific or engineering
knowledge of the phenomenon being studied. State any limitations
or assumptions of the model.
4. Conduct appropriate experiments and collect data to test or
validate the tentative model or conclusions made in steps 2 and 3.
5. Refine the model on the basis of the observed data.
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:4

6. Manipulate the model to assist in developing a solution to the

problem.
7. Conduct an appropriate experiment to confirm that the proposed
solution to the problem is both effective and efficient.
8. Draw conclusions or make recommendations based on the problem
solution.
Note: Several iterations of these steps (especially steps 2–4) may be
required to obtain the final solution.
Consequently, engineers must know how to efficiently plan experi-
ments, collect data, analyze and interpret the data, and understand
how the observed data are related to the model they have proposed for
the problem under study.
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:5

1.2. Why Engineers Study Probability and

Statistics?
1.2.1. Probability vs. Statistics
• Probability models are theoretical models of the occurrence of
uncertain events.
At the most basic level, in probability, the properties of certain
types of probabilistic models are examined.
In doing so, it is assumed that all parameter values that are needed
in the probabilistic model are known.
• Statistics is about empirical data and can be broadly defined as a
set of methods used to make inferences from a known sample to a
larger population that is in general unknown.
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:6

• In studying probability, we follow much the same routine as in the

study of other fields of mathematics.
• Statistics is based on inductive reasoning. More specifically,
given a sample of data (i.e., observations), we make generalized
probabilistic conclusions about the population from which the data
are drawn or the process that generated the data.
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:7

1.2.2. Why Engineers Study Statistics

• The field of statistics deals with the collection, presentation,
analysis, and use of data to make decisions, solve problems, and
design products and processes.
• Because many aspects of engineering practice involve working with
data, obviously some knowledge of statistics is important to any
engineer.
• Specifically, statistical techniques can be a powerful aid in designing
new products and systems, improving existing designs, and
designing, developing, and improving production processes.
• For this reason, we studied basic concepts of probability in the last
semester. We are going to learn statistics in this course.
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:8

1.3. Motivated Examples

Example 1.1 (Quality Control Problem).
• A certain bakery produces 100-gram packages of cookies. Hence,
the bakery stands to lose money when the population mean
µ > 100 grams and the customer loses out when µ < 100 grams.
• To check whether the true average weight of the packages is
100 grams, they select a random sample of 25 packages and find
that their mean weight is x̄ = 98.8 grams.
• Suppose that it is known from experience that the standard
deviation of the weight of the packages of cookies is 2.5 grams.
• Is the production under control on a given day at 5% significant
level (i.e., with at most 5% errors).
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:9

Example 1.2 (Customer’s Concern).

• Suppose that it is known from experience that the standard
deviation of the weight of 100-gram packages of cookies made by a
certain bakery is 2.5 grams.
• A customer is concerned about the weight of the 100-gram packages
of cookies she is buying from the manufacturer.
• She takes a random sample of 25 packages from her stock and finds
that their mean weight is x̄ = 98.8 grams.
• Is the customer justified in complaining at 5% significant level?
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:10

Example 1.3 (Comparing Two Means).

• The management of a supermarket would like to know if its female
customers spend more money, on average, than its male customers.
• They have collected random samples of 56 female customers and 58
male customers.
• The collected data shows that on average, female customers
spend $102, with a standard deviation $43. Male customers
spend $90 on average, with a standard deviation $56.
• Can we say that the mean spending of female customers is more
than that of male customers at 5% significant level?
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:11

Example 1.4 (Comparing the Means of Matched Pairs).

• A manufacturer is concerned about the loss of weight of ceramic
parts during a baking step.
• The readings before and after baking, on the same specimen, are
naturally paired.
• It would make no sense to compare the before-baking weight of one
specimen with the after-baking weight of another specimen.
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:12

Example 1.5 (Statistics in Polls).

• A political poll shows that 58 persons of a random sample of
100 citizens favor Candidate A, whereas 42 persons would vote
for Candidate B.
• It is claimed that the two candidates are tied.
• Is the claim justifiable at 5% significant level.
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:13

Example 1.6 (Statistics in Polls).

• It is found that 132 of 200 voters in District A favor a given
candidate for election to the United States Senate and 90 of
150 voters in Distinct B favor this same candidate.
• Find a range with 95% confidence that (p1 − p2) (i.e., the difference
between the actual proportions of voters from the two districts who
favor the candidate) is within that range.
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:14

Example 1.7 (Comparison of the Effectiveness of Two Medicines).

• 200 patients were randomly assigned to two equal groups; one group
received medicine 1, and the other received medicine 2.
• After eight weeks, 27 of the medicine-1-treated patients showed
improvement, whereas 19 of those treated with medicine 2
improved.
• Is there any difference between the effectiveness of the two medicines
at 5% significant level?
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:15

Example 1.8 (Quality Control Problem).

• An automatic filling machine is used to fill bottles with soft drink/
liquid detergent/ · · ·
• If the standard deviation of fill volume is too large, an unacceptable
proportion of bottles will be under- or overfilled.
• A random sample of 20 bottles results in a sample standard
deviation of fill volume of s = 1.23 (milliliters).
• Find the upper bound for σ with 95% confidence level.
Chi-Kong Ng, ENGG2780B, Dept. of SEEM, CUHK 1:16

Example 1.9 (Manufacturing Problem).

• It is desired to determine whether there is less variability in the
silver plating done by Machine 1 than in that done by Machine 2.
• If independent random samples of size 12 of the two machines’ work
yield s1 = 0.040 mil and s2 = 0.062 mil, can we say that σ12 < σ22
at 5% significant level?