College of Engineering, Qatar University
Page 1 of 8
Probability and Statistics, GENG200
2
B
Tutorial - 9
Question
Sections 9-1
Page 303:
1)
9-3
2)
9-4
3)
9-5
Answer:
9-3
a)
nm
H
nm
H
20
:
,
20
:
1
0
<
=
σ
σ
b)
This result does not provide strong evidence that the standard deviation has not been
reduced. This result says
that we do not have enough evidence to reject the null
hypothesis
. It is not support for the null hypothesis.
9-4
a)
Newtons
H
Newtons
H
25
:
,
25
:
1
0
<
=
μ
μ
b)
No, this results only means that we do not have enough evidence to support
H
1
9-5
a)
α
= P(reject H
0
when H
0
is true)
= P(
X
≤
11.5 when
μ
= 12) =
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
≤
−
4
/
5
.
0
12
5
.
11
/
n
X
P
σ
μ
= P(Z
≤
−
2)
= 0.02275.
The probability of rejecting the null hypothesis when it is true is 0.02275.
b)
β
= P(accept H
0
when
μ
= 11.25) =
(
)
25
.
11
5
.
11
=
>
μ
when
X
P
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
>
−
4
/
5
.
0
25
.
11
5
.
11
/
n
X
P
σ
μ
=
P(Z > 1.0)
= 1
−
P(Z
≤
1.0) = 1
−
0.84134 = 0.15866
The probability of accepting the null hypothesis when it is false is 0.15866.
c)
β
= P(accept H
0
when
μ
= 11.25) =
=
(
)
5
.
11
5
.
11
=
>
μ
when
X
P
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
>
−
4
/
5
.
0
5
.
11
5
.
11
/
n
X
P
σ
μ
= P(Z > 0) = 1
−
P(Z
≤
0) = 1
−
0.5 = 0.5
The probability of accepting the null hypothesis when it is false is 0.5

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