Actual State of Affairs
The UNKNOWN TRUTH
H
0
is TRUE
H
0
is FALSE
Decision
Do not reject H
0
Correct Decision
Type II Error
Reject H
0
Type I Error
Correct Decision

OIS 2340
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Business Statistics
Estimating Population Parameters
5
Three Methods for Conducting a Hypothesis Test
1. Compare a test-statistic computed from the sample data with a critical z-value (or t-value)based upon the level of significance. (Note: t-values are used when the population standard deviation is unknown.)
z
z

OIS 2340
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Business Statistics
Estimating Population Parameters
6
2. Compare a sample statistic (x-bar or p-bar) to a critical test statistic valuethat corresponds to the upper or lower confidence limit.
Critical Test Statistic Value for Mean (σ known):
z
n
Critical Test Statistic Value for Mean (σ unknown):
t
n
Critical Test Statistic Value for Proportion:
1
z
n
ADVANTAGE:
Includes the original contextual units.
Example:
Consider the following hypothesis test:
H
o
:
µ = 15
H
A
:
µ ≠ 15
A sample of 50 provided a sample mean of 14.15.
The population standard deviation is
3.
Use α = 0.05.

OIS 2340
–
Business Statistics
Estimating Population Parameters
7
3.
Use the
p-value
.
The
p-value
is the
observed
level of significance, or the
actual
probability of making a Type I error.
ADVANTAGE: Easy with technology.
DISADVANTAGE:
More complicated without technology.
Example:
Consider the following hypothesis test:
H
o
:
µ > 80
H
A
:
µ < 80
A sample of 100 provided a sample mean of 75.5.
The population standard deviation is
12.
Use α = 0.01.

OIS 2340
–
Business Statistics
Estimating Population Parameters
8

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- Fall '11
- Statistics, Statistical hypothesis testing, Type I and type II errors