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ENGR 610 - Applied Statistics
Exam #1
Name ___________________________
This is an open-book, open-note exam, to be taken outside of class, without consultation.
This is part one of a two-part exam and is to be completed without the use of any
software, although the use of a simple calculator is permissible. Mark or put all answers
for this portion of the exam on these sheets if possible (preferably in electronic form).
Show all your work! Any additional pages should have your name on them and have
your work and answers identified by question number.
A person’s age in whole years would be considered what kind of variable?
1.
a. Categorical
b. Discrete
c. Continuous
Which measurement scale type best describes a person’s age?
2.
a.
b.
c.
d.
Nominal
Ordinal
Interval
Ratio
The following table contains the ages of some youth at a gathering. Answer the
following questions (3-8) regarding this data. Use the empty columns and rows in the
table as needed to show your work.
#
Age
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
8
9
10
11
13
13
8
7
9
10
14
10
8
10
12
11
9
10
10
12
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ENGR 610 - Applied Statistics
Exam #1
3.
Name ___________________________
What are the following?
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.
Arithmetic average (mean) = ________
Minimum = ________
Maximum = ________
Range = ________
Mid-range = ________
Mode = ________
Q1 = ________
Q2 (median) = ________
Q3 = ________
Inter-quartile range = ________
Mid-hinge = ________
Variance = ________
Standard deviation = ________
4.
Sketch and label a frequency distribution (histogram) plot
5.
Sketch and label a Box-and-Whisker plot
6.
How would you best describe the above distribution?
a. Symmetric
b. Skewed left
c. Skewed right
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ENGR 610 - Applied Statistics
Exam #1
7.
Name ___________________________
What are the Z values for Q1, Q2 (median), and Q3 above?
Z(Q1) =________, Z(Q2) =________, Z(Q3) =________
What should they be for a normal distribution?
Z @ 0.25 =________, Z @ 0.50 =________, Z @ 0.75 =________
Does the distribution of ages appear normal?
8.
If the above data were actually a sample drawn from a larger population, what
would the sample variance be?
s2 = ________
9.
Given the following as the most general case for events A and B:
P(A or B) = P(A) + P(B) – P(A)P(B|A)
a. What is P(A)P(B|A) equivalent to, and what is it called?
b. What is P(B|A) called?
c. Under what condition would P(A or B) = P(A) + P(B) – P(A)P(B) ?
d. Under what additional condition would P(A or B) = P(A) + P(B) ?
e. Under what additional condition would P(A or B) = 1 ?
10.
The table below (on next page) contains a discrete probability distribution for
some ages. Answer the following questions regarding this data. Use the empty
columns and rows as needed to show your work
a. What is the expectation (average) value for Age? ________
b. What is the expectation value for its variance? ________
c. Does this distribution look familiar? How so?
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ENGR 610 - Applied Statistics
Exam #1
Age
6
7
8
9
10
11
12
13
14
11.
P(Age)
1 / 21
1 / 21
3 / 21
3 / 21
6 / 21
2 / 21
2 / 21
2 / 21
1 / 21
Consider a normal deck of 52 playing cards. Draw 5 cards at random.
a.
b.
c.
d.
e.
12.
Name ___________________________
What is the probability that exactly 3 of them will be Hearts? ________
What is the probability that at least 1 of them will be a King? ________
What is the probability that all of them will be Black? ________
What will be the average number of Diamonds? ________
What will be the variance in number of Red cards? ________
Given the same deck of cards, what probability distribution would you use
a. for successive hands drawn from the same deck without replacement?
b. for predicting the position of the first occurrence of a particular card?
c. for predicting the x-th occurrence of a particular card type on the n-th draw?
13.
What probability distribution would you use to predict
a. the number of discrete events over a continuous interval of time given the
average occurrence over this time interval?
b. the time between such events?
14.
Given a normal distribution of ages (which may be considered fractional and
continuous) with a mean of 10 and standard deviation of 2, what age-range
contains the middle 95% of the population?
________ - ________
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ENGR 610 - Applied Statistics
Exam #1
15.
Name ___________________________
If you were to randomly and exhaustively sample, 4 at a time, the population of
ages above (in question 14).
a. What will be the average sample mean? ________
b. What will be the standard error (deviation) of the sample mean? ________
16.
What probability distribution are you apt to encounter for values that range
several orders of magnitude?
17.
A process is considered under statistical control if only _____________ causes of
variation are in effect.
18.
The WECO rules and the observation of non-random patterns in a control chart
are used to detect ______________ causes of variation.
19.
np and p charts are based on the ____________________ probability distribution?
20.
What would be the upper and lower control limits for a p chart where the average
proportion of non-conformities is 0.1 and the sample size is 9?
UCL = ________, LCL = ________
21.
c and u charts are based on the ____________________ probability distribution?
22.
What would be the upper and lower control limits for a c chart where the average
rate of non-conformities is 9 per unit?
UCL = ________, LCL = _________
23.
The __ chart or the ___ chart is most often used along side X-bar charts to
monitor variability. The ___ chart is better for larger sample sizes (n > 10).
24.
A _____________ chart is often used to help set control limits for an individual X
chart when there is no standard deviation available.
25.
Given a sample of size of 9 with a sample mean of 10.0 and a sample variance of
4.0 (population variance is unknown), what is
a. the 95% confidence interval for the population mean?
b. the 95% confidence interval for the population variance?
c. the 95% prediction interval for a future individual value?
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ENGR 610 - Applied Statistics
Exam #1
Name ___________________________
This is part two of a two-part exam. You are expected to use Excel and the PHStat addin wherever possible on this portion of the exam. It is preferred that any results from
Excel be pasted as tables into this document, along with explanations.
26.
Using the MPG data in the file Auto96.xls on the CD, compute the following
descriptive statistics:
Arithmetic Mean
Mode
Quartiles (Q1, Q3)
Range
Variance
Median
Midrange
Midhinge
Interquartile Range
Standard Deviation
27.
Generate a Box-and-Whisker plot for the MPG data.
28.
Generate a histogram plot using 5 MPG intervals (15-40).
29.
Generate a Paretto diagram using the same 5 MPG intervals.
30.
Generate a normal probability plot. Is the MPG data normally distributed?
31.
How would you best describe the MPG distribution?
32.
Assuming that the above MPG data is only a sample taken from a larger
population, what are the 95% confidence interval estimates for the population
mean, the standard deviation, and a single future value?
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ENGR 610 - Applied Statistics
Exam #1
Name ___________________________
It is preferred that this entire completed exam be e-mailed to the instructor sometime
prior to the next class time. It may also be printed and turned in at the beginning of class.
This page, however, should be printed, signed, and turned in at the beginning of the next
class.
Address from which exam was e-mailed : _____________________________________
Filename(s), if e-mailed: ___________________________________________________
Address(es) to which exam was e-mailed :
 [email protected]
 [email protected]
 [email protected]
Signature: ____________________________________
(Verifying that this exam was completed as instructed and without consultation)
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