Ass#6

```COURSE: ENGINEERING PROBABILITY &amp; STATISTICS
ASSIGNMENT #6
Lecturer: Ho Thanh Vu
Student: PhαΊ‘m NhαΊ­t T&acirc;n
-ID :IEIEIU16002
-Class: Friday morning
Question 1:
Let π = ππ£πππππ πππ‘π‘πππ¦ ππππ. We want to test whether the new process affects π or not
Let π»0 : π = 125
π»1 : π ≠ 125
We have:
πΜ = 131 βππ’ππ  ; π = 39 &gt; 30 ; π  = 11 βππ’ππ
πΜ −π
131−125
ππ‘ = π / π0 = 11/√39 = 3.406 =&gt; p-value is 2*(1-0.9997)=0.0006
√
πΌπ πΌ = 0.05 ⇒ ππΌ/2 = &plusmn;1.96 &lt; 3.406 =&gt; ππππππ‘ π»0 =&gt; π‘βπ ππππππ π  ππππππ‘π  πππ‘π‘πππ¦ ππππ
πΌπ πΌ = 0.01 ⇒ ππΌ/2 = &plusmn;2.57 &lt; 3.406 =&gt; ππππππ‘ π»0 =&gt; π‘βπ ππππππ π  ππππππ‘π  πππ‘π‘πππ¦ ππππ
Both cases give very significant results
Question 2:
Let π = ππ£πππππ βπππβπ‘ ππ πππ ππ ππππ‘πππ
Let π»0 : π ≥ π0 = 170
π»1 : π &lt; π0 = 170
Sample information:
πΜ = 171.283 ππ ; π = 20 &lt; 30 ; π  = 3.829 ππ, df=19
πΜ − π0 171.283 − 170
π‘π‘ =
=
= 1.4985
π /√π
3.829/√20
πΌπ πΌ = 0.01 ⇒ π‘πΌ;19 = −2.539 &lt; 1.4985 =&gt; ππ πππ‘ ππππππ‘ π»0
πΌπ πΌ = 0.05 ⇒ π‘πΌ;19 = −1.729 &lt; 1.4985 =&gt; ππ πππ‘ ππππππ‘ π»0
Therefore, the average height of men in Vietnam is more than or equal to 170cm
Question 3:
Let π = π π’πππ’π ππππ‘πππ‘ ππ ππππ ππ ππ’ππ
Let π»0 : π ≤ π0 = 0.15
π»1 : π &gt; π0 = 0.15
We have:
πΜ = 0.162 πππππππ‘π  ; π = 40 &gt; 30 ; π  = 0.040 ππ; πΌ = 0.05
πΜ − π0 0.162 − 0.15
ππ‘ =
=
= 1.8974
π /√π
0.040/√40
πΌπ πΌ = 0.05 ⇒ ππΌ = 1.65 &lt; 1.8974 =&gt; ππππππ‘ π»0 =&gt; the sulfur content in the diesel fuel is actually larger
than 0.15 percent.
Question 4:
Patient
1
2
3
4
5
6
7
8
9
10
11
Before
134
122 132 130 128
140 118
127 125
142 137
After
Difference
140
6
130 135 126 134
8
3
-4
6
138 124
-2
6
126 132
-1
7
144 137
2
0
12
13
14
15
16
136 130
139 128
128
144 137
8
7
143 146
4
18
149
21
πΏππ‘ ππ· = ππ΄ − ππ΅ . We want to test if this drug changes blood pressure so:
Let π»0 : ππ· = 0
π»1 : ππ· ≠ 0
Μ = 5.563 ; π = 16 &lt; 30 ; π π· = 6.603; πΌ = 0.05 ; ππ = 15
Sample information: πΜ = π·
πΜ − 0
5.563 − 0
π‘π‘ =
=
= 3.37
π π· /√π 6.603/√16
πΌπ πΌ = 0.05 ⇒ π‘πΌ;15 = &plusmn;2.131 &lt; 3.37 =&gt; ππππππ‘ π»0 ⇒ this drug actually changes blood pressure
2
Question 5:
Let π»0 : π ≥ 0.45
π»1 : π &lt; 0.45
49
πΜ =
= 0.392
125
πΜ − π0
0.392 − 0.45
ππ‘ =
=
= −1.31
π
∗
(1
−
π
)
0.45
∗
0.55
0
0
√
√
π
125
πΌπ πΌ = 0.05 ⇒ ππΌ = −1.65 &lt; −1.31 =&gt; π·π πππ‘ ππππππ‘ π»0
Therefore, the program doesn’t reduce the proportion of executives who show signs of the crisis
Question 6:
Let π»0 : π ≥ 0.95
π»1 : π &lt; 0.95
1380
πΜ =
= 0.92
1500
πΜ − π0
0.92 − 0.95
ππ‘ =
=
= −1.686
π
∗
(1
−
π
)
0.95
∗
0.05
0
0
√
√
π
1500
πΆβπππ π πΌ = 0.05 ⇒ ππΌ = −1.65 &gt; −1.686 =&gt; ππππππ‘ π»0
Therefore lower interest rates for mortgages during the following period actually reduced the percentage of
households living in rental units.
Question 7:
π = 25; π  2 = 175; πΌ = 0.05
Assume the population is normally distributed
Let π»0 : π 2 ≤ 156
π»1 : π 2 &gt; 156
(π − 1)π  2 24 ∗ 175
π π‘=
=
= 26.923
π2
156
πΉππ πΌ = 0.05 ⇒ πΆπππ‘ππππ π£πππ’ππ  ππ  π 2 (24,0.05) = 36.42 &gt; 26.923 βΉ π·π πππ‘ ππππππ‘ π»0
Therefore, we can’t prove that the variance is above the required level, corrective action should not be taken.
2
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