Ass#6

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COURSE: ENGINEERING PROBABILITY & STATISTICS
ASSIGNMENT #6
Lecturer: Ho Thanh Vu
Student: Phạm Nhật Tân
-ID :IEIEIU16002
-Class: Friday morning
Question 1:
Let  =   . We want to test whether the new process affects  or not
Let 0 :  = 125
1 :  ≠ 125
We have:
̅ = 131 ℎ ;  = 39 > 30 ;  = 11 ℎ
̅ −
131−125
 = / 0 = 11/√39 = 3.406 => p-value is 2*(1-0.9997)=0.0006
√
  = 0.05 ⇒ /2 = ±1.96 < 3.406 =>  0 => ℎ    
  = 0.01 ⇒ /2 = ±2.57 < 3.406 =>  0 => ℎ    
Both cases give very significant results
Question 2:
Let  =  ℎℎ    
Let 0 :  ≥ 0 = 170
1 :  < 0 = 170
Sample information:
̅ = 171.283  ;  = 20 < 30 ;  = 3.829 , df=19
̅ − 0 171.283 − 170
 =
=
= 1.4985
/√
3.829/√20
  = 0.01 ⇒ ;19 = −2.539 < 1.4985 =>    0
  = 0.05 ⇒ ;19 = −1.729 < 1.4985 =>    0
Therefore, the average height of men in Vietnam is more than or equal to 170cm
Question 3:
Let  =     
Let 0 :  ≤ 0 = 0.15
1 :  > 0 = 0.15
We have:
̅ = 0.162  ;  = 40 > 30 ;  = 0.040 ;  = 0.05
̅ − 0 0.162 − 0.15
 =
=
= 1.8974
/√
0.040/√40
  = 0.05 ⇒  = 1.65 < 1.8974 =>  0 => 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
  =  −  . We want to test if this drug changes blood pressure so:
Let 0 :  = 0
1 :  ≠ 0
̅ = 5.563 ;  = 16 < 30 ;  = 6.603;  = 0.05 ;  = 15
Sample information: ̅ = 
̅ − 0
5.563 − 0
 =
=
= 3.37
 /√ 6.603/√16
  = 0.05 ⇒ ;15 = ±2.131 < 3.37 =>  0 ⇒ this drug actually changes blood pressure
2
Question 5:
Let 0 :  ≥ 0.45
1 :  < 0.45
49
̂ =
= 0.392
125
̂ − 0
0.392 − 0.45
 =
=
= −1.31

∗
(1
−

)
0.45
∗
0.55
0
0
√
√

125
  = 0.05 ⇒  = −1.65 < −1.31 =>    0
Therefore, the program doesn’t reduce the proportion of executives who show signs of the crisis
Question 6:
Let 0 :  ≥ 0.95
1 :  < 0.95
1380
̂ =
= 0.92
1500
̂ − 0
0.92 − 0.95
 =
=
= −1.686

∗
(1
−

)
0.95
∗
0.05
0
0
√
√

1500
ℎ  = 0.05 ⇒  = −1.65 > −1.686 =>  0
Therefore lower interest rates for mortgages during the following period actually reduced the percentage of
households living in rental units.
Question 7:
 = 25;  2 = 175;  = 0.05
Assume the population is normally distributed
Let 0 :  2 ≤ 156
1 :  2 > 156
( − 1) 2 24 ∗ 175
 =
=
= 26.923
2
156
  = 0.05 ⇒     2 (24,0.05) = 36.42 > 26.923 ⟹    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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