Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
12.77
12.95 a.
Let x1 = sales volume
Let x2 = 1 if NW, 0 if not
Let x3 = 1 if S, 0 if not
Let x4 = 1 if W, 0 if not
The complete second order model for the sales price of a singlefamily home is:
E(price) = 0 + 1x1 + 2x12 + 3x2 + 4x3 + 5x4 + 6x1x2 + 7x1x3
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
13.89 a.
Open data file
SPC>Control Charts>Basic Variables Charts>Xbar and R
Range Chart for Day
12
10
9.27
Range
8
6
4.63
4
2
0
0.00
0
4
8
12
Subgroup
16
20
24
Based on the Rchart, the process is out of control for the day shift. There are two point
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
7.41 H0:
=0
Ha:
0
LOS = 0.01
the true mean pointspread error for all NFL games does not differ from zero
the true mean pointspread error for all NFL games differs from zero
n = 240
xbar = 1.6
s = 13.3
xbar has a tdistribution with
239 degrees of fre
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
Chapter 14
Exponential smoothing
it can either be used for smoothing a data set or
it can be used as a forecasting technique
t
Yt Smoothed value
1 Y1 S1 = Y1
2 Y2 S2 = Y2 + (1 ) S1 = Y2 + (1 ) Y1
3 Y3 S3 = Y3 + (1 ) S2 = Y3 + (1 ) (Y2 + (1 ) Y1) = Y3 +
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
Chapter 2
Standard Notations
Sample
x
Mean
Standard Deviation
s
Variance
s2
Sample Size
n
Measure
Mean (Average OR Expected Value)
Population
2
N
Central Tendency Measure
Formula
n
i=1 xi
Description
Balance Point
n
Median
x(n+1) even sample size
Middle V
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
4.93 a
Pr( 10 x 12)
=
Pr(10 < x < 12)
=
Describe > Distribution Fitting > Probability Distribution
Pr(x < 12)  Pr(x < 10)
Right Click (Over the Cumulative Distribution Output) > Pane Options
Lower Tail Area (<)
Variable Dist. 1
Dist. 2
10 0.308536
12
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
Chapter 8
We have two different populations. Therefore, we take two samples, one from each
population.
We want to answer the question: Is some parameter in one population different from the
corresponding parameter in the other population?
Paired (matched,
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
Chapter 7
Conclusion\ True State of Nature
H0 True
Ha True
Accept H0 (Assume H0 True)
Correct decision
Type II error (probability )
Reject H0 (Assume Ha True)
Type I error (probability )
Correct decision
Hypothesis
A hypothesis is a statement about a para
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
Chapter 12 (part 2)
Incorporating categorical variables into regression
Use indicator variables (dummy variables) when categories are nonordered.
Indicator variable:
o Takes only two values, usually yes (1) and no (0)
o If you have n categories (i.e. le
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
Chapter 10
One Way Table
Test: Chi squared
Hypothesis
H0: pi = p0,i for all i
Ha: at least one of the pis does not equal to its
hypothesized value
TwoWay (Contingency) Table
Test: Chi squared
Hypothesis
Ho: The two classifications are independent
Ho:
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
Chapter 13
Control Charts:
1. Run Chart: Graphically shows trends and changes in the data over time (X time, Y
measurement of interest recorded). Points are connected with a straight line. The
graph includes a center line used to search for patterns.
ch
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
Chapter 11
Simple Regression
Two variables
The dependent variable (Y) is the variable of interest
o we would like some mechanism for predicting the value (or expected value)
of the dependent variable
Independent variable (X)
o we also have information
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
8.37 a.
sample 1 before
sample 2 after
H0:
Ha:
1 > 2
population1
population2
1  2 0 the new policy did not reduce the mean number of complaints
1  2 > 0 the new policy reduced the mean number of complaints
Compare > Two Samples > Pared Samples
Right C
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
Chapter 4
Continuous
Distributions
Discrete Distributions
Type
Distribution
Binomial Distribution: Bin(p,n)
p = probability of success
n = sample size
=
Number of successes in a sample of n observations (trails)
Poisson: Poisson()
=
Events per unit (time,
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
Chapter 12 (part 1)
Multiple regression
one dependent variable (Y) continuous, and measured on an interval scale
potentially many independent variables (X1, X2, , Xk), not just one, as in simple
regression
Y = 0 + 1*X1 + 2*X2 + + k*Xk +
Population reg
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
9.32 a.
b.
completely randomized
honey, DM, control (no dosage)
H0:
H = DM = C
the mean improvement scores for a
at least two 's arethe
notmean
equalimprovement scores diffe
LOS not specified, use the (0.01, 0.1) default rule
Ha:
Open the data file
Compar
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
Chapter 6
Target Parameter
p
Estimation
Point
Interval
Name
Mean/ Average/ Expected Value
Proportion/ Percentage Factor/ Rate
Type of Data
Quantitative
Qualitative
Information
Gives NO information about the closeness to
unknown population parameter.
Gives
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
Analysis of Variance ANOVA
Comparing means of three or more groups under the assumption that
each of the groups follows a normal distribution
the groups all have the same variance
Oneway ANOVA
one factor
Blocked design
extended paired sample comparison
t
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
11.99 a.
b.
c.
d.
e
f.
Plot>Scatterplots>XY Plot
Plot of Index vs Salary
790
Index
690
590
490
390
290
0
2
4
Salary
6
8
(X 10000)
The scattergram appears to show some decrease in the index as salary increases
Relate>One Factor>Simple Regression
Depen
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
10.17 Day
MON
TUE
WED
THR
FRI
SAT
SUN
Volume
Number observed
0.191
0.198
0.187
0.18
0.155
0.043
0.046
90
82
72
70
51
18
31
414
p1=.191 and p2=.198 and p3=.187 and p4=.18 and
H0:
p5=.155 and p6=.043 and p7=0.046
the number of overweight trucks per week is
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
6.17 a.
b.
c.
yes
xbar
Describe>Numeric Data>OneVariable Analysis
(50 randomly selected salaries are obtained a
=
?
Count
Average
Standard deviation
Coeff. of variation
Minimum
Maximum
Range
Stnd. skewness
Stnd. kurtosis
xbar
d.
Open the original dat
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
3.39 a
C
W
F
A
I
oil structure is caission
oil structure is well protector
oil structure is fixed platform
oil structure is active
oil structure is inactive
Freq
A
I
Total
C
c
Pr(A)
=
Pr(AC) + Pr(AW) + Pr(AF)
d
Pr(W)
=
Pr(AW) + Pr(IW)
e
Pr(IC)
=
f
Pr(I or
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
14.22 a
Describe>Time Series>Smoothing
Data Table for SP500
First smoother: EWMA with smoothing constant = 0.3
Second smoother: none
Period
Q1/04
Data
Smooth Rough
1126.2
1126.2
0
Q2/04
Q3/04
Q4/04
Q1/05
Q2/05
Q3/05
Q4/05
Q1/06
Q2/06
Q3/06
Q4/06
Q1/07
Q
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
9.98 a.
response =
weight of a brochure
factor(s) =
1 factor, carton
treatments =
five different cartons
experimental units =
brochures
the distributions of weights in each carton should be normal
the distributions of weights should all have the same vari
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
11.23 Relate>One Factor>Simple Regression
Simple Regression  Revenue (millions) vs. TweetRate
Dependent variable: Revenue (millions)
Independent variable: TweetRate
Linear model: Y = a + b*X
Coefficients
Least SquaStandard T
Parameter Estimate Error
St
Statistical Analysis: Uncertainty, Prediction and Qualilty Improvement
BQOM 2401

Fall 2016
A
1
2
3
4
5
6
B
8.40 Population 1
Population 2
7
8
9
10
11
C
D
E
F
G
H
I
J
K
L
M
N
O
P
crashes before camera installation
crashes after camera installation
This is a paired sample comparison
To see if a ttest is valid, test the differences for normality