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Stat312: Sample Midterm II.
Moo K. Chung
[email protected]
March 25, 2003
1. Consider the sample of fat content of 10 randomly
selected hot dogs: 25, 21, 22, 17, 29, 25, 16, 20,
19, 22. Suppose that these are from a normal pop
ulation.
We want to test if the fat content of hot
dogs is 23.
(a) State the null and alternate hypotheses
(5
points).
(b) What is your test statistic and a rejection rule at
95
%
level? (5 points)
(c) Is the fat content of hot dogs 23? Explain your
result (5 points).
(d) Compute the probability of type I error when
you do the hypothesis test using the test statistic in
(b). Explain your result (5 points).
(e) Define the
P
value and compute the
P
value
for using the test statistic in (b) (5 points).
>X<c(25,21,22,17,29,25,16,20,19,22)
>sum(X)
[1] 216
> var(X)
[1] 15.6
> qnorm(c(0.025,0.05))
[1] 1.96 1.64
> qt(0.025,c(9,10))
[1] 2.26 2.23
> pt(c(1.0,1.1,1.2,1.3,1.4,1.5),9)
[1] 0.83 0.85 0.87 0.89 0.90 0.92
Solution.
(a) Let
μ
be the population mean of the
fat content in hot dogs. Then
H
0
:
μ
= 23
and
H
1
:
μ
6
= 23
. (b) Since the population variance
is unknown, the test statistic should be the
t
statis
tic given by
T
= (
¯
X

μ
)
/
(
S/
√
10)
. Note that
t
0
.
025
,
9
= 2
.
26
. So we reject
H
0
if

T

>
2
.
26
. (c)
s
2
= 15
.
6
. The
t
value is
t
= (¯
x

23)
/
(
s/
√
10) =

1
.
12
. Since the value is not in the rejection re
gion, we do not reject
H
0
. So we may assume that
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This homework help was uploaded on 01/31/2008 for the course STAT 312 taught by Professor Chung during the Fall '04 term at Wisconsin.
 Fall '04
 Chung
 Statistics

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