Statistical Inference Solutions
1
Confidence Intervals and Plug-in Predictive Intervals
There is concern about the speed of automobiles traveling over a particular stretch of highway. For
a random sample of n = 7 automobiles, radar indicated the following
Practice Questions Solutions
Suppose we are considering building a portfolio with a mix of the following assets and their projected
returns:
Risk-free bond = 0.006
Stock X1 N (0.01, 0.005)
Stock X2 N (0.02, 0.01)
1. Calculate the descriptive statistics
Process Formulas
Process time:
Per unit processing time:
PT =
n
X
P P Ti = ci +
ti
i=1
Cycle time (workstation):
STi
B
Lead time for workstation:
Li =
ti
ci =
mi
W IPi
demand
Production lead time:
Cycle time (system):
LT =
csystem = max ci
Takt tim
Regression Formulas
1
Determining the Regression Equation
Slope:
CVXY
VX
b=
or
b = RXY
SY
SX
Intercept:
a = Y bX
Explanatory (predictive) power (R2 ):
R-squared =
SSR
SST
Standard deviation of the model (Se ):
r
SSE
Se =
dfSSE
2
or
R-squared =
s
or
Se
Statistical Inference Formulas
1
Standard Error and Confidence Intervals
Standard error for the sample mean:
95% confidence interval for the sample mean:
SX
CI = X 2
n
SX
SE =
n
Standard error for p:
r
SE =
2
95% confidence interval for p:
r
p (1 p)
Quality Solutions
1
The Bernoulli and Binomial Distributions
A manufacturing company that fabricates parts for the aerospace industry has just received an
order for two special parts (call them X and Y ).
Let X = 1 if product X is defective, and 0 otherw
Process 2 Solutions
1
Value Stream Mapping
Precision Manufacturing, Inc. (PMI) manufactures assembly brackets for two major automotive
customers. The manufacturing process is shown below:
Process Step 1
Forming
Task time = 12 seconds
Setup time = 3 minute
Process 1 Solutions
1
Process Analysis
Assume you are managing a process that needs to produce 100 bagel sandwiches with veggies on
them. After some experimentation, you find out that the tasks involved take approximately the
following times:
Cutting (0.
Regression Solutions
1
Understanding the Simple Linear Regression Model
The data in this question are returns on two portfolios called SMB and HML. These portfolios
were made famous by Eugene Fama and Kenneth French and have been widely used by finance
pr
Queuing Theory Solutions
1
The M/M/s Queuing Model
A small movie theater complex has a single ticket booth cashier who can maintain an average
service rate of 280 moviegoers per hour. Arrivals on a typically active day are on average 210 per
hour. To dete
Process Definitions
Process: any part of an organization that takes inputs and transforms them into outputs or a network
of activities with a specific starting and ending point, that repeats itself
Flowchart: a graphical way to describe the process; a p
Exam 2 Formulas
Service time:
Mean of a Binomial distribution:
1
ts = conversion factor
E[Y ] = np
Variance of a Binomial distribution:
Utilization factor:
=
s
V [Y ] = np(1 p)
95% Predictive Interval (individual outcome):
Number in system:
(
L=
s
Exam
Name_
TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.
1)
1) A plan that relates to a specific area of a business, such as marketing, is known as a strategic
plan.
Answer:
True
False
2)
2) A plan that relates to a spe
Exam
Name_
TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.
1) Finance is any transaction where money is exchanged for goods and services.
Answer:
True
1)
False
2)
2) Finance is any transaction where money is exchanged for