Download STA 291-021 Summer 2007

Lecture 20
Dustin Lueker

The p-value for testing H1: µ≠100 is p=.001.
This indicates that…
1.
2.
3.
4.
There
There
There
There
is
is
is
is
strong
strong
strong
strong
evidence
evidence
evidence
evidence
that
that
that
that
μ=100
μ≠100
μ>100
μ<100
STA 291 Fall 2009 Lecture 20
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
The p-value for testing H1: µ≠100 is
p=.001. In addition you know that the test
statistic was z=3.29. This indicates that…
1. There is strong evidence that μ=100
2. There is strong evidence that μ>100
3. There is strong evidence that μ<100
STA 291 Fall 2009 Lecture 20
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
Range of values such that if the test statistic
falls into that range, we decide to reject the
null hypothesis in favor of the alternative
hypothesis
◦ Type of test determines which tail(s) the rejection
region is in
 Left-tailed
 Right-tailed
 Two-tailed
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
Testing µ
x  0
t
s n
◦ Without the aide of some type of technology it is
impossible to find exact p-values when using this
test statistic, because it is from the t-distribution
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
An assumption for the t-test is that the
population distribution is normal
◦ In practice, it is impossible to be 100% sure if the
population distribution is normal
 It may be useful to look at histogram or stem-and-leaf plot
(or normal probability plot) to check whether the normality
assumption is reasonable

Good news
◦ t-test is relatively robust against violations of this
assumption
 Unless the population distribution is highly skewed, the
hypotheses tests and confidence intervals are valid
 However, the random sampling assumption must never be
violated, otherwise the test results are completely invalid
STA 291 Fall 2009 Lecture 20
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

A courier service advertises that its average
delivery time is less than 6 hours for local
deliveries. A random sample of times for 12
deliveries found a mean of 5.6875 and a
standard deviation of 1.58. Is this sufficient
evidence to support the courier’s
advertisement at α=.05?
State and test the hypotheses using the
rejection region method
 What would be the p-value if we used that method?
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

Thirty-second commercials cost $2.3 million
during the 2001 Super Bowl. A random sample
of 116 people who watched the game were asked
how many commercials they watches in their
entirety. The sample had a mean of 15.27 and a
standard deviation of 5.72. Can we conclude
that the mean number of commercials watched is
greater than 15?
State the hypotheses, find the test statistic and
p-value for testing whether or not the mean has
changed, interpret
◦ Make a decision, using a significance level of 5%
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

Similar to testing one proportion
Hypotheses are set up like two sample mean
test
◦ H0:p1=p2
 Same as H0:p1-p2=0

Test Statistic
z
( pˆ 1  pˆ 2 )  ( p1  p2 )
pˆ 1 (1  pˆ 1 ) pˆ 2 (1  pˆ 2 )

n1
n2
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
Government agencies have undertaken surveys of
Americans 12 years of age and older. Each was
asked whether he or she used drugs at least once
in the past month. The results of this year’s
survey had 171 yes responses out of 306
surveyed while the survey 10 years ago resulted
in 158 yes responses out of 304 surveyed. Test
whether the use of drugs in the past ten years
has increased.
State and test the hypotheses using the rejection
region method at the 5% level of significance.
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