A certain vehicle emission inspection station advertises that the wait time for customers is less than 6 minutes. A local resident wants to test this claim and collects a random sample of 64 wait times for customers at the testing station. He finds that the sample mean is 5.51 ​minutes, with a standard deviation of 2.3 minutes. Does the sample evidence support the inspection​ station's claim? Use the α=0.005 level of significance to test the advertised claim that the wait time is less than 6 minutes.

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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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A certain vehicle emission inspection station advertises that the wait time for customers is less than
6
minutes. A local resident wants to test this claim and collects a random sample of
64
wait times for customers at the testing station.
He
finds that the sample mean is
5.51
​minutes, with a standard deviation of
2.3
minutes. Does the sample evidence support the inspection​ station's claim? Use the
α=0.005
level of significance to test the advertised claim that the wait time is less than
6
minutes.
What are the hypotheses for this​ test?
 
H0​:
 
muμ
pp
sigmaσ
 
greater than>
not equals≠
less than<
equals=
nothing
minutes
H1​:
 
sigmaσ
muμ
pp
 
less than<
greater than>
not equals≠
equals=
nothing
minutes
​(Type an integer or a​ decimal.)
What is the value of the test​ statistic?
 
 
t 0t0
z 0z0
=nothing
​(Round to two decimal places as​ needed.)
What is the​ P-value?
 
​P-value=nothing
​(Round to three decimal places as​ needed.)
Use the
α=0.005
level of significance to test the advertised claim.
 
Since the​ P-value is
 
greater
less
than
α​,
 
do not reject
reject
the null hypothesis. There
 
is not
is
sufficient evidence to conclude that the mean wait time is less than
6
minutes. In other​ words, the evidence
 
supports
does not support
the advertised claim.
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