2.
(TCO 11)  A restaurant claims that its speed of service time is less than 18 minutes. A random selection
of 36 service times was collected, and their mean was calculated to be 17.1 minutes. Their standard
deviation is 3.1 minutes. Is there enough evidence to support the claim at alpha = .08. Perform an
appropriate hypothesis test, showing each important step.
(Note:
1st Step:
Write Ho and Ha; 2nd Step:
Determine Rejection Region; etc.)
(
)
)
,
18
:
18
)
,
0.08
)
1.751
1.751
17.1
18
)
1.5
3.1/ 6
)
1.5
1.751,1.751 ,
i Null hypothesis
Alternative hypothesis
ii significance level
iii reject the null hypothesis if z
or greater than z
iv z
v As z
is
lies in
so we cannot reject
µ
µ
α
=
<
=
< −
>
−
=
= −
= −
−
A restaurant claims that its speed of service time is less than 18 minutes
is
Wrong
the null hypothesis
Inotherword
4.
(TCO 1,7) A social service worker wants to estimate the true proportion of pregnant teenagers who miss
at least one day of school per week on average.
The social worker wants to be within 3% of the true
proportion when using a 95% confidence interval.
A previous study estimated the population proportion at
0.28.
(a).
Using this previoius study as an estimate for p, what sample size should be used?
(b).
If the previous study was not available, what estimate for p should be used?
(
)
(
)
(
)(
)
/ 2
2
2
/ 2
1
)
1.96
1
0.28
1
0.28
860.51
861
0.03
)
0.5
p
p
a E
Z
n
Z
n
p
p
E
b estimate for p should be
α
α
−
=
⇒
=
−
=
−
=
≈
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 Spring '08
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 Statistics, Normal Distribution, Standard Deviation, Statistical hypothesis testing, µ

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