QMDS200 STATISTICS AND DATA ANALYSIS
Assignment # 3
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Chapter7
GoalProgrammingandMultiple
ObjectiveOptimization
1
Introduction
Most of the optimization problems considered
to this point have had a single objective.
Two other modeling techniques:
Goal Programming (GP): no one specific objective
function but r
Chapter 6
Integer Programming
Introduction
When one or more variables in an LP problem
must assume an integer value we have an
Integer Linear Programming (ILP) problem.
ILPs occur frequently
Scheduling workers
Manufacturing airplanes
Integer variables als
Suggested Solutions
1.
2. Let X = no. of customers who purchased a particular coupon special
N = 2000
n = 50
X = 894.50
= 121.25
unknown population distribution of X
n = 50 > 30 Central Limit Theorem
Sampling distribution of is approximately normal.
a)
Examples:
1. An orange juice producer buys all his oranges from a large orange orchard. The
amount of juice squeezed from each of these oranges is assumed to be normally
distributed with a mean of 4.70 ounces and a standard deviation of 0.40 ounce.
Suppos
Chapter 8
Confidence Interval Estimation
There are two types of estimates for unknown population parameters:
1. Point estimate: consists of a single sample statistic value which is used to estimate the
true population parameter value.
2. Interval estimate
QMDS SATISTICS AND DATA ANALYSIS
Assignment # 3
Suggested Solutions
1.
Textbook, Problem 8.47, p.307
Let X = number of companies that informally monitored social networking sites to stay
on top of information related to their company
n = 500
315
p = 500 =
Chapter 9
Fundamentals of Hypothesis Testing: One-Sample Tests
Hypothesis testing is a procedure based on sample evidence and probability theory to
determine whether the hypothesis is a reasonable statement and should not be rejected, or
is unreasonable a
Examples:
1. A representative of a community group claims that the average income per
household in the area is $25,000. Suppose that for the type of area involved
household income can be assumed to be approximately normally distributed, and
the standard d
Suggested Solutions
1. Let X = household income
1 = first community
2 = second community
H0: 1 2 = 0
H1: 1 2 0
= 5%
Both population distributions are normal Sampling distribution of ( X 1 X 2 ) is normal.
n1 = 30 & n 2 = 40
X 1 = 35500 & X 2 = 34600
1 =
Examples:
1. A developer is considering two alternative sites for a regional shopping center.
Since household income in the community is one important consideration in such
site selection, he wishes to perform the test that there is no difference between
Chapter 10
Two-Sample Tests and One-Way ANOVA
In Topics 8 and 9, we learned how to obtain confidence intervals and perform hypothesis tests for one population parameter (, , or 2).
Frequently, however, inferential statistics is used to compare the paramet
Suggested Solutions
1. Let X = income per household in the area
H0: = 25000
H1: 25000
= 5%
n = 15
=24000
= 2000
Population distribution of X is normal.
Sampling distribution of is normal.
Test statistic: Z STAT =
X
X
Decision rule: Reject H0 if ZSTAT