Test
Just for fun, here are some multiplechoice
test questions. Green belts, black belts and technical people using
statistical methods should be able to answer such questions. For
each question there is only one correct answer. Good luck!
1. A doctor prescribed two tablets per day for
a patient. The drug content of each tablet has a normal distribution
with mean = 50 mg and standard deviation = 4 mg. What is the standard
deviation of drug taken by the patient per day?
 4
 2
 4
 8
 8
2. To compare two treatments in terms of their
mean, what is the approximate sample size per treatment if the difference
in mean to be detected is equal to the standard deviation, the alpharisk
is 5% and the betarisk is 10%?
 10
 20
 30
 35
 40
3. Regression analysis was used to obtain the
following equation relating response Y to input factors A and B.
Y = 100 + 3A – 0.5B + error
The % confidence associated with both coefficients
in the equation exceeded 95% and the Rsquare value turned out to
be 20%. Which of the following statements is not true?
 B has a small but statistically significant
effect on Y
 Measurement error must be small to find this
small effect of B
 A has a statistically significant effect on
Y
 Some other factor is influencing Y
 Measurement error may be large
4. Why do variable charts occur in pairs (e.g.
Xbar and R) and attribute charts occur singly (e.g. p)?
 Variable data are more precise
 Both mean and variance can be computed for
variable data but not for attribute data
 Variance is a deterministic function of mean
for the attribute data
 Attribute data have only two categories, knowing
one you know the other
 None of the above
5. Given the same data, five students computed
the values of Cp, Cpk, Pp and Ppk indices. Which computations are
likely to be correct?

Cp 
Cpk 
Pp 
Ppk 
a 
2 
1.5 
1.33 
1.0 
b 
1.5 
1.7 
1.42 
1.0 
c 
2.0 
1.0 
0.62 
0.5 
d 
1.82 
1.0 
1.47 
1.2 
e 
Both a and c above 
6. From an Xbar chart, variance within subgroup
was found to be 2 and variance between subgroups was found to be
0.1. What action should be taken to significantly improve the process?
 Eliminate time trend
 Eliminate shifttoshift differences
 Supplier needs to improve batchtobatch variability
 Measurement system variability should be evaluated
 Remove cycling along the time axis
7. A and B are fixed factors in a twolevel factorial
experiment, the two levels of each factor being –1 and +1.
Analysis of the factorial experiment resulted in the following equation
Y = 10 + 4A + 3B + error
What is the variance component due to factor A?
 40
 8
 12
 4
 16
8. A hamburger chain had five fast food restaurants.
A different group of ten randomly selected people was sent to each
restaurant (a total of 50 people) and each person evaluated the
quality of two hamburgers. What is the structure for this data collection
scheme?
 Restaurants and people are crossed and hamburgers
are nested
 All three variables are crossed
 People and hamburgers are crossed but are nested
inside restaurants
 Hamburgers are nested inside people who are
nested inside restaurants
 None of the above
9. If W represents half the width of a twosided
specification, to achieve six sigma quality, the standard deviation
of measurement should be less than which of the following?
 W
 W/2
 W/4
 W/8
 W/12
