Answer:
z(s) is in the acceptance region. We accept H₀ we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine
Step-by-step explanation:
We must evaluate the differences of the means of the two machines, to do so, we will assume a CI of 95%, and as the interest is to find out if the new machine has better performance ( machine has a bigger efficiency or the new machine produces more units per unit of time than the old one) the test will be a one tail-test (to the left).
New machine
Sample mean x₁ = 25
Sample variance s₁ = 27
Sample size n₁ = 45
Old machine
Sample mean x₂ = 23
Sample variance s₂ = 7,56
Sample size n₂ = 36
Test Hypothesis:
Null hypothesis H₀ x₂ - x₁ = d = 0
Alternative hypothesis Hₐ x₂ - x₁ < 0
CI = 90 % ⇒ α = 10 % α = 0,1 z(c) = - 1,28
To calculate z(s)
z(s) = ( x₂ - x₁ ) / √s₁² / n₁ + s₂² / n₂
s₁ = 27 ⇒ s₁² = 729
n₁ = 45 ⇒ s₁² / n₁ = 16,2
s₂ = 7,56 ⇒ s₂² = 57,15
n₂ = 36 ⇒ s₂² / n₂ = 1,5876
√s₁² / n₁ + s₂² / n₂ = √ 16,2 + 1.5876 = 4,2175
z(s) = (23 - 25 )/4,2175
z(s) = - 0,4742
Comparing z(s) and z(c)
|z(s)| < | z(c)|
z(s) is in the acceptance region. We accept H₀ we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine
The very hight dispersion of values s₁ = 27 is evidence of frecuent values quite far from the mean
When rounding here are the rules
If the next number to the right is 1-4, you will round down or keep the # the same.
If the next number to the right is 5-9, you will round up to the next number.
So with your # 281,421,906
a. hundred million. This is the first 2...the number to the right of it is 8, so we will round the 2 up. And the answer is 300,000,000
b. ten million. This is the 8...the number to the right of it is 1, so we will round it down and 8 will remain an 8. And the answer is 280,000,000
c. million. This is the first 1 (281)...the number to the right is 4, so we will round down and 1 will remain a 1. And the answer is 281,000,000
d. hundred thousand. This is the 4...the number to the right of it is 2, so we will round down and the 4 will remain a 4. And the answer is 281,400,000
e. thousand. This is the second 1 (281,421)...the number to the right is the 9, so we will round up and the 1 will become a 2. And the answer is 281,422,000
Now for #14, think about the rules.
1. If you round it to the nearest one, you get 7.
2. If you round it to the nearest tenth, you get 7.0.
3. If you round it o the nearest hundredth, you get 7.00
4. It is the least number that fits the clues.
Ok basically it is saying, it rounds up to 7. So what would be the number that would round UP to 7? That would be 6. I'm rounding UP because it says it is the LEAST number that fits the clues.
Answer:
A- 0.125
B- Success of climbing mount Everest is independent of age.
Step-by-step explanation:
A.
Let x denote success in climbing Mount Everest
Let y denote the climber is at least 60 years old.
Therefore,
P(x) = 0.31
P(y) = 0.04
P( x ∩ y) = 0.005
Probability of success when the climber is at least 60 years old =
P( x ∩ y) ÷ P(y) = 0.005 ÷ 0.04 = 0.125.
B.
The success rate is independent of age as there are both success and failure rates across board on the scale of ages of climbers.
8x+40+124= 180
8x + 164= 180
8x = 16
x = 2
D is the answer to the question
54/72 gets reduced to 27/36 by the number 2 :)
