Sample problems for midterm 1
There will be 4 problems on the test similar (and possibly a bit easier, but deﬁnitely not
harder) to the problems below.
1. An automotive company needs an adhesive with a bond strength in excess of 3500 N/cm
2
.
A test of 20 samples of adhesive produced by a potential supplier gave a sample mean of
3650 N/cm
2
and a sample standard deviation of 280 N/cm
2
. Will this result satisfy the auto
motive company if they are looking for strong evidence? Formulate the relevant hypothesis
and test at
α
= 0
.
05. Using the ttable, bound the corresponding Pvalue.
Solution.
They would like to be able to show conclusively that
μ >
3500. Therefore,
the hypothesis that they need to test is
H
0
:
μ
= 3500 versus
H
1
:
μ >
3500. The relevant
test statistic is
t
0
=
¯
x

μ
0
s/
√
n
=
3650

3500
280
/
√
20
= 2
.
40
.
The corresponding critical value is
t
0
.
05
,
19
= 1
.
73, and, since
t
0
> t
0
.
05
,
19
, one can reject
H
0
which amounts to existence of strong evidence in favor of the bond strength exceeding 3500
N/cm
2
. Using the ttable, we see that
t
0
.
025
,
19
< t
0
< t
0
.
01
,
19
. This implies that for the
Pvalue we have 0
.
01
< P <
0
.
025.
2. The probability theorist believes that the temperature of his tea (
T
) is distributed
uniformly between 60 and 70 degrees. Let
f
(
t
) denote the corresponding pdf, and
F
(
t
) be
the cdf. Find the following quantities.
a)
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 Spring '08
 Perevalov
 Statistics, Standard Deviation, Statistical hypothesis testing, Sample standard deviation

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