Lecture #3
Learning Objectives
1.
Learn how to formulate hypotheses about a population mean.
2.
Know how to conduct a test of significance about a population mean
when the sampling distribution of
X
is Normal and
σ
is known
a.
Using a
P
value.
b.
Using
the “significance region” or “critical value” method.
c.
Using a confidence interval estimate.
3.
Be able to state appropriate conclusions about the population mean
and the specific business problem based on the results of an
hypothesis test.
4.
Know the errors that can be made when conducting an hypothesis
test.
5.
Know the definition of the following terms:
Null Hypothesis
Alternative Hypothesis
Critical Value
Level of Significance
TwoTail Test
Type I Error
OneTail Test
Type II Error
p
value
“I have no special talent.
I am only passionately curious.”

Albert Einstein (1879 – 1955)
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BM330  Lecture 3
Hypothesis Tests About the Population Mean
(Independent sample observations,
X
~Normal,
σ
known)
Example 1
:
Revisiting
Unlimited Avenue
In Lectures 1 and 2, we discussed the proposed chain of upscale stores
designed to market highend woman’s fashions called
Unlimited Avenue
.
We need to evaluate the annual household income in a given market
location. It has been stated that the average household income needed to
make the store location successful must exceed $50,000 per year.
Recall that the market research staff at the Limited collected a random
sample of 64 households from the geographical area in question and found
an average annual income of $50,725. We assumed that the standard
deviation for household incomes is $4,200.
At issue is which of the two following possibilities is more likely:
1.
μ
≤
$50,000, i.e., the mean annual income does not exceed $50,000
2.
μ
> $50,000, i.e., the mean annual income exceeds $50,000
1