Example
: A random sample of 400 individuals who filed a tax return between
April 10 and April 15 (the last five days to file returns) had a sample mean
refund of $910 with a sample standard deviation of $1600. What is a 95%
confidence interval for the average refund for those who file returns in the
last 5 days?
Now
: Individuals who file taxes before the last 5 days (prior to April 10)
have an average refund of $1056. A researcher suggests that the reason indi
viduals wait until the last five days is that on average these individuals receive
lower refunds than do early filers. Does the data support this hypothesis?
To answer questions like this we will use a statistical inferential technique
called
hypothesis testing
.
1
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Hypothesis Tests
•
We want to determine whether a statement about the value of the pop
ulation parameter should or should not be rejected.
•
We first make a tentative assumption about the population called the
null hypothesis, denoted by
H
0
.
•
We define another hypothesis called the alternative hypothesis, denoted
by
H
a
, that is the opposite of the null hypothesis.
•
We then use data collected from a sample to test the two competing
statements.
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 Fall '10
 Jager,AbigailL
 Standard Deviation, Null hypothesis, Statistical hypothesis testing, H0, researcher, Type I and type II errors, alternative hypotheses

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