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Hypothesis Tests for
μ
 Known
σ
OneTailed Tests
Lower Tail Test
H
0
:
μ
≥
μ
0
H
a
:
μ < μ
0
Upper Tail Test
H
0
:
μ
≤
μ
0
H
a
:
μ > μ
0
Example
: Individuals ﬁling federal income tax returns prior to March 31 re
ceived an average refund of $1056. Consider the population of “lastminute”
ﬁlers who mail their tax return during the last ﬁve days of the income tax
period (April 10 to April 15). A researcher suggests that a reason individuals
wait until the last ﬁve days is that on average these individuals receive lower
refunds than do early ﬁlers. We want to test this claim.
For a sample of 400 individuals who ﬁled a tax return between April 10
and April 15, the sample mean refund was $910. Based on prior experience
a population standard deviation of
σ
= $1600 may be assumed.
1. Specify the null and alternative hypotheses.
Ex
:
1
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View Full Document 2. Specify the probability of making a Type I error. This number is de
noted by
α
and is called the level of signiﬁcance.
Ex
:
3. Compute the test statistic.
•
The test statistic is a measure of how far the sample mean ¯
x
is from
the hypothesized value
μ
0
.
•
We use the sampling distribution of ¯
x
to obtain the test statistic.
•
The sampling distribution of
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This note was uploaded on 01/24/2011 for the course STATISTICS 19897 taught by Professor Jager,abigaill during the Fall '10 term at Kansas State University.
 Fall '10
 Jager,AbigailL

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