Download STA 291 Summer 2010

Lecture 18
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 Summer 2010 Lecture 18
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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 Summer 2010 Lecture 18
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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 with n large
x  0
z
s n
◦ Just like finding a confidence interval for µ with n
large
 Reasons for choosing test statistics are the same as
choosing the correct confidence interval formula
STA 291 Summer 2010 Lecture 18
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
Testing µ with n small
x  0
t
s n
◦ Just like finding a confidence interval for µ with n
small
 Reasons for choosing test statistics are the same as
choosing the correct confidence interval formula
 Note: It is difficult for us to find p-values for this test
statistic because of the way our table is set up
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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
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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 5.7 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.
◦ Why wouldn’t the p-value method be good to use?
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
Results of confidence intervals and of twosided significance tests are consistent
◦ Whenever the hypothesized mean is not in the
confidence interval around the sample mean, then
the p-value for testing H0: μ=μ0 is smaller than 5%
(significance at the 5% level)
 Why does this make sense?
◦ In general, a 100(1-α)% confidence interval
corresponds to a test at significance level α
STA 291 Summer 2010 Lecture 18
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

A survey of 35 cars that just left their
metered parking spaces produced a mean of
18 minutes remaining on the meter and a
standard deviation of 22. Test the parking
control officer’s claim that the average time
left on meters is equal to 15 minutes.
State and test the hypotheses with a level of
significance of 5% using the confidence
interval method.
STA 291 Summer 2010 Lecture 18
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