CHAPTER 06—STATISTICAL METHODS IN QUALITY MANAGEMENT
TRUE/FALSE
1. Statistics is a science concerned with the collection, organization, analysis, interpretation, and
presentation of data.
2. The collection of all possible outcomes of an experiment is called an event.
3. Probability is the likelihood that an outcome occurs.
4. The sum of the probabilities over all possible outcomes must be between 0 and 1.
5. Two events are independent if they have no outcomes in common.
6. A random variable is a theoretical description of the outcome of an experiment.
7. The Poisson distribution is closely related to the binomial distribution.
8. The number of defects observed in a sample is an example of a continuous random variable.
9. The probability density function for the normal distribution is,
.
10. Often, the positively skewed data can be transformed to a normal distribution by using a mathematical
transformation such as taking logarithms.
11. Products are boxed in groups of 25. Drawing a sample of boxes and inspecting all units in the boxes
selected is an example of systematic sampling.
12. The median is the observation that occurs most frequently.
13. The variance is the simplest measure of dispersion and is computed as the difference between the
maximum value and the minimum value in the data set.
14. Distributions with values of coefficient of kurtosis (CK) greater than 3 are more flat with a wide
degree of dispersion.
15. The Data Validation Toolpak in Microsoft Excel for Windows provides many procedures for
conducting statistical analyses.
16. A frequency distribution is a table that shows the number of observations in each of several
nonoverlapping groups.
17. The Histogram tool provides the basic statistical measures of location, dispersion, and shape.
18. One of the major disadvantages of the Histogram tool is that the results are not dynamically linked to
the data.
19. As the sample size increases, the standard error of the mean increases, all else being held constant.
20. A confidence interval is a point estimate of a population parameter.
21. All else being equal, as the confidence level increases, the confidence interval becomes larger
to provide higher levels of assurance that the interval contains the true population parameter.
22. In hypothesis testing, the null hypothesis, H0, is assumed to be false in the absence of contradictory
data.
23. Correlation is a measure of a linear or a non-linear relationship between two variables.
24. The square of the correlation coefficient is called the coefficient of determination.
25. In general, an experiment with m factors at k levels would have km combinations.
26. When interactions are present in an experiment, main effects have little meaning.
MULTIPLE CHOICE
1. Statistical methods help managers make sense of data and gain insight about the:
a.
ability of using statistics and quality tools in daily work.
b.
nature of variation in all processes.
c.
nature of variation in the processes they manage.
d.
technology used for data analysis and visualization.
2. The collection of all possible outcomes of an experiment is called the _____.
a.
event
b.
population
c.
sample space
d.
random variable
3. The conditional probability of an event A given that event B is known is given by:
a.
.
b.
.
c.
.
d.
.
4. A _____ is a function that assigns a numerical value to every possible outcome in a sample space.
a.
probability distribution
b.
population parameter
c.
sample statistic
d.
random variable
5. A _____ can take on any real value over a specified interval of real numbers.
a.
sample space
b.
continuous random variable
c.
discrete random variable
d.
probability distribution
6. If a normal random variable has a mean = _____ and a standard deviation = _____, it is called a
standard normal distribution.
a.
1;0
b.
1;1
c.
0;0
d.
0;1
7. A perfume bottle is designed to have a capacity of 15 ounces. There is variation in the bottle
manufacturing process. Based on historical data, let’s suppose that the bottle capacity can be
reasonably modeled by a normal distribution with a mean of 15 ounces and a standard deviation of 0.2
ounces. What proportion of these bottles will have a capacity between 14.7 and 15.1 ounces?
a.
0.3830
b.
0.6247
c.
0.8664
d.
0.9876
8. The _____ distribution models the time between randomly occurring events.
a.
normal
b.
Poisson
c.
exponential
d.
binomial
9. The component of statistical methodology that includes the collection, organization, and
summarization of data is called:
a.
descriptive statistics.
b.
probability distribution.
c.
statistical inference.
d.
predictive statistics.
10. _____ is the process of drawing conclusions about unknown characteristics of a population from
which data are taken.
a.
Descriptive statistics
b.
Regression analysis
c.
Statistical inference
d.
Correlation analysis
11. Which of the following is NOT a type of sampling scheme?
a.
Stratified sampling
b.
Biased sampling
c.
Cluster sampling
d.
Judgment sampling
12. Which of the following requires the opinion of an expert to determine the location and characteristics
of a definable sample group?
a.
Judgment sample
b.
Simple random sample
c.
Systematic sample
d.
Stratified sample
13. Partitioning a population into hierarchical groups or levels, and selecting a sample from each group is
known as:
a.
simple random sampling.
b.
stratified sampling.
c.
systematic sampling.
d.
cluster sampling.
14. The sampling method where every item in the population has an equal probability of being selected is
called:
a.
simple random sampling.
b.
cluster sampling.
c.
systematic sampling.
d.
judgment sampling.
15. A typical group is selected from the population, and a random sample is taken from within the group.
This is an example of _____ sampling.
a.
simple random
b.
stratified
c.
cluster
d.
judgment
16. If random samples are not used, _____ may be introduced.
a.
quality control
b.
bias
c.
testing
d.
probability
17. Any sampling procedure can result in _____ types of errors.
a.
two
b.
three
c.
four
d.
five
18. Any sampling procedure can result in two types of errors: _____ error and _____ error.
a.
standard; variable
b.
simple; conditional
c.
random; measurement
d.
sampling; systematic
19. Which of the following constitutes an approach to reducing sampling error?
a.
Providing statistical training to workers at all organizational levels
b.
Using user-friendly software for data analysis and visualization
c.
Taking a larger sample from the population
d.
Planning the sampling study carefully
20. A _____ is a subset of objects taken from the _____.
a.
population; sample
b.
cluster; strata
c.
sample; population
d.
sample space; experiment
21. Calculating the average value of 5 sample measurements of a door width is an example of:
a.
descriptive statistics.
b.
hypothesis testing.
c.
regression analysis.
d.
design of experiments.
22. Which of the following is NOT a tool for descriptive statistics?
a.
Frequency distribution
b.
Regression analysis
c.
Proportion
d.
Histogram
23. Given here are a set of sample data: 12.0, 18.3, 29.6, 14.3, and 27.8. The sample standard deviation for
this data is equal to _____.
a.
62.895
b.
7.931
c.
7.093
d.
50.316
24. The _____ measures the degree of asymmetry of observations around the mean.
a.
coefficient of correlation
b.
coefficient of skewness
c.
coefficient of kurtosis
d.
coefficient of determination
25. Group width =
a.
(UL – LL)/Number of Groups.
b.
Number of Groups/(UL – LL).
c.
(UL + LL)/Number of Groups.
d.
(UL – LL)(Number of Groups).
26. A sample of size 16 is randomly selected from a population of size 90. Determine the standard error of
the mean if the population standard deviation equals 20.
a.
2.11
b.
4.16
c.
4.56
d.
5.00
27. Everything else remaining constant, when the sample size increases:
a.
the variance decreases.
b.
the variance increases.
c.
the variance is unaffected.
d.
the variance could increase or decrease.
28. The approximation to a normal distribution can be assumed for sample sizes of _____.
a.
15
b.
20
c.
25
d.
30 or more
29. Based on historical data, the diameter of a ball bearing is normally distributed with a mean of 0.527
cm and a standard deviation of 0.008 cm. Suppose that a sample of 18 ball bearings are randomly
selected from a very large lot. Determine the probability that the average diameter of a sampled ball
bearing is greater than 0.530 cm.
a.
0.2324
b.
0.4938
c.
0.5062
d.
0.0559
30. A manager at a local manufacturing company has been monitoring the output of one of the machines
used to manufacture chromium shells. Past data indicate that if the machine is functioning properly,
the length of the shells produced by this machine can be modeled as being normally distributed with a
mean of 118 centimeters and a standard deviation of 6.3 centimeters. Suppose 10 shells produced by
this machine are randomly selected. What is the probability that the average length of these 10 shells
will be between 116 and 120 centimeters when the machine is operating “properly?”
a.
0.2709
b.
0.2943
c.
0.9656
d.
0.6826
31. A travel article reasearcher randomly sampled 250 adult residents of Illinois and asked each resident if
he/she planned to vacation outside of Illinois this coming summer. Fifty-six of these adults responded
that they plan to vacation outside of Illinois. What is the 95% confidence interval for the population
proportion of adult residents of Illinois who plan to vacation outside of Illinois this coming summer?
a.
(0.178, 0.318)
b.
(0.246, 0.250)
c.
(0.172, 0.276)
d.
(0.142, 0.354)
32. A government report gives a 99% confidence interval for the proportion of welfare recipients who
have been receiving welfare benefits for more than 5 years to be 21% 4.5%. Which of the following
intervals could not be a 95% confidence interval for the proportion of welfare recipients who have
been receiving welfare benefits for more than 5 years?
a.
21% 4.2%
b.
21% 3.76%
c.
21% 3.9%
d.
21% 4.8%
33. A testing engineer in a light bulb factory is planning a study to estimate the average life of a large
shipment of light bulbs. The engineer wants to estimate the average life within plus or minus 16 hours
with 95 percent confidence. Assuming a process standard deviation of 90 hours, determine the sample
size for this study.
a.
7
b.
43
c.
58
d.
122
34. _____ involve(s) drawing inferences about two contrasting propositions relating to the value of a
population parameter, one of which is assumed to be true in the absence of contradictory data.
a.
Probability distributions
b.
Hypothesis testing
c.
Descriptive statistics
d.
Predictive statistics
35. The rejection region is chosen so that the probability of the test statistic falling into it, if H0 is true, is
_____.
a.
b.
c.
d.
36. _____ is a methodology for drawing conclusions about equality of means of multiple populations.
a.
Quality analysis
b.
Analysis of variance
c.
Correlation analysis
d.
Regression analysis
37. In ANOVA, by dividing the mean square between groups by the mean square within groups, a(n)
_____ statistic is computed.
a.
t
b.
z
c.
F
d.
R2
38. Suppose that a scatter diagram depicts a relationship between the two variables that can be
summarized by a straight line. The correlation coefficient is computed and results in a value of -0.73.
Which of the following is NOT TRUE?
a.
There is a linear relationship between the two variables.
b.
In general, an increase in one variable is associated with an increase in the other variable.
c.
In general, an increase in one variable is associated with a decrease in the other variable.
d.
Even though the correlation coefficient is less than zero, it still communicates the strength
of the linear relationship.
39. Three scatter diagrams are given below. How many of the diagrams present data that can be described
by a linear relationship and, therefore, justifiably summarized by the correlation coefficient?
Plot A
Plot B
Plot C
a.
Plot A
b.
Plot B
c.
Plot A and Plot B
d.
Plot A and Plot C
40. In regression analysis, _____ measures the proportion of the variation in the dependent variable that is
explained by the independent variable(s).
a.
coefficient of correlation
b.
an F statistic
c.
coefficient of determination
d.
regression equation
41. _____ is a test or series of tests that enables the experimenter to compare two or more methods to
determine which is better or determine levels of controllable factors to optimize the yield of a process
or minimize the variability of a response variable.
a.
Designed experiment
b.
Hypothesis testing
c.
Kurtosis
d.
Regression
42. One of the most common types of experimental designs in which all combinations of levels of each
factor are considered is called a(n) _____ experiment.
a.
combination
b.
factorial
c.
interaction
d.
simple
43. In a factorial experiment, each combination of different levels of the factor is called a(n) _____.
a.
main effect
b.
response
c.
treatment
d.
interaction
44. An experiment that evaluates the effect of two temperatures (100 and 200 degrees F) and two reaction
times (45 and 95 minutes) on process yield has _____ possible combinations to test.
a.
2
b.
4
c.
6
d.
8
45. In a designed experiment, a(n) _____ measures the difference that a factor has on the response.
a.
main effect
b.
factorial
c.
treatment
d.
interaction
ESSAY
1. What is probability? What are its characteristics?
2. What are the rules that apply when calculating probabilities of events?
3. Define binomial and Poisson distributions. State their probability functions.
4. Briefly discuss the relation between exponential distribution and Poisson distribution with an example.
5. The times (in minutes) required by a sample of 15 students to complete a class assigment are given
below:
45, 42, 56, 54, 40, 37, 39, 45, 49, 43, 45, 50, 49, 55, 48
Using Excel functions and calculate the mean, median, mode, range, sample variance, and sample
standard deviation.
6. In Excel’s Histogram tool, how are bins defined?
ANS:
7. What is a sampling distribution? State the sampling distributions of and p for finite populations.
8. State the steps involved in a hypothesis test.
ANS:
9. A manager was assigned the task of investigating the error in payments for routine purchases made by
the purchasing department. The manager randomly selected 12 payments, investigated them
thoroughly, and determined the payment error for each of these payments. The payment error was
defined as the difference between the amount paid and what should have been paid. The payment
errors determined for these selected payments were as follows:
$17
$25
$14
–$10
$20
$40
$35
$30
$28
$22
$15
$16
a. What is the 95% confidence interval for the population mean payment error?
b. Suppose a recent company report inferred that the mean payment error may be running as high as
$25. That led the manager to test the null hypothesis that the population mean payment error is
equal to $25 versus the alternative that the population mean payment error is not equal to $25.
Using a level of significance equal to 0.01, perform this hypothesis test.
c. Suppose another manager used this same data to test the null hypothesis that the population mean
payment error is less than or equal to $15 versus the alternative that the population mean payment
error is greater than $15. What is the test statistic for this hypothesis testing situation? What is the
critical value at a level of significance equal to 0.01? What is the conclusion?
CASE
1. What are the typical soldering defects in a wave soldering process of a PCA-Encoder?
ANS:
2. In which of the following companies, a high level of soldering defects was observed, necessitating 100
percent inspection for all circuit boards?
a. GE Fanuc Company
b. Hewlett-Packard
c. Branch-Smith, Inc.
d. Berton Card Company
3. What are the aspects of the wave soldering process that might affect the resulting quality of the
PCA-Encoders?
ANS:
4. To improve the quality of the wave soldering process through design of experiments, _____ factors at
_____ levels were selected for the experiment.
a. seven; two
b. six; three
c. seven; three
d. three; two
5. Briefly explain how the experiment was conducted.
ANS:
6. Using _____, it was observed that bath temperature, wave height, and omega had a significant effect
on the soldering defects.
a. hypothesis testing
b. cluster sampling
c. descriptive statistics
d. analysis of variance
7. Why were additional experimental designs conducted to reduce soldering defects in the process?
8. Explain how the new experiment was conducted to reduce soldering defects in the process.
9. What was the objective of the Black Belt Project #P52320 investigated by a team at the GE Fanuc
manufacturing plant?
10. What are the tools and databases identified by the team to be used in the study?
11. Based on a _____-step process flowchart, it was decided that the analysis would require the use of a
moderately complex experimental design in the Six Sigma project.
a. 27
b. 28
c. 29
d. 30
12. The team identified _____ characteristics (Xs, or independent variables) that were considered
important to measure during the experiment for each of the _____ finish types (Ys, or dependent
variables).
a. 3; 13
b. 29; 8
c. 8; 6
d. 13; 3
13. What was the primary hypothesis stated by the team? What is the additional hypothesis investigated?
14. Of 15 ANOVA analysis runs performed on the 13 experimental variables that were measured in the
Six Sigma project, why did 8 experimental variables showed no significance?
15. What is the conclusion arrived by the team of the Six Sigma project at GE Fanuc manufacturing plant?