Paired t-test Application (Part 1)An environmental engineer is tasked with determining whether a power plant cooling system is heating the water it uses more than allowed by environmental regulations. They measure water temperatures at the cooling system input and the cooling system output for several different days in several different seasons. A data file containing these measurements is Fin_PTA.csvPreview the document. Do a statistical analysis on this data to determine if the temperature change between the input and output of the cooling system is different than 6 degrees. What does your analysis indicate
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Complete Question
The complete question is shown on the first and second uploaded image
Answer:
Part 1
The correct option is B
Part 11
The correct option is H
Step-by-step explanation:
From the question we are told that
The sample size is n = 15
Generally the sample mean for the input temperature is mathematically represented as
[tex]\= x _1 = \frac{\sum x_i}{n}[/tex]
[tex]\= x _1 = \frac{57.6 + 68.9 \cdots +60.4 }{15}[/tex]
[tex]\= x _1 = 62.57 [/tex]
Generally the sample mean for the output temperature is mathematically represented as
[tex]\= x _2 = \frac{\sum x_i}{n}[/tex]
[tex]\= x _2 = \frac{65.1 + 74.4 \cdots +67.3 }{15}[/tex]
[tex]\= x _2 = 55.97 [/tex]
Generally the difference between the mean of the input temperature and that of the output temperature is
[tex]d = \= x_1 - \= x_2[/tex]
=> [tex]d = 62.57 - 55.97 [/tex]
=> [tex]d = 6.6[/tex]
Generally the standard deviation of the difference between the input temperature and the output temperature is mathematically represented as
[tex]s_d = \sqrt {\frac{1}{n-1 } \sum [d_i - d]^2}[/tex]
=> [tex]s_d = \sqrt{\frac{[(57.6 - 65.1) - 6.6]^2+[(68.9 - 74.4) - 6.6]^2+ \cdots +[(68.1 - 74.7) - 6.6]^2 }{15-1} }[/tex]
=> [tex]s_d = 1.732 [/tex]
The null hypothesis is [tex]H_o : \mu_1 -\mu_2 = 6[/tex]
The alternative hypothesis is [tex]H_a : \mu _1 - \mu_2\ne 6[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{d - 6}{ \frac{s_d}{ \sqrt{n} } }[/tex]
[tex]t = \frac{6.6- 6}{ \frac{1.732}{ \sqrt{15} } }[/tex]
[tex]t = 1.342[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 * P(t > 1.342)[/tex]
From the student t distribution table( reference - danielsoper(dot)com(slash)statcalc(slash)calculator) at a degree of freedom of df = n-1 = 15-1 = 14
[tex]P(t > 1.342) = t_{1.342 , 14} = 0.100478[/tex]
So
[tex]p-value = 2 * 0.100478)[/tex]
[tex]p-value = 0.201[/tex]
From the values obtained we see that the [tex]p-value > \alpha[/tex] hence the decision rule is fail to reject the null hypothesis
The conclusion is
The cooling system changes the temperature of the water by 6 degrees.
Related Questions
Six of 8 stores have power drinks on sale saturday. In simplest form, what fraction of the stores has power drinks on sale saturday?
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Please help me with this problem
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Answer:
Since the taxis are heading directly towards each other, we will assume the path between them to be a straight line
We have 2 taxis coming towards each other, which means that we have 2 observers in this system
so from now on, we will see this situation from the eyes of the driver coming at the speed of 40mph
Now imagine yourself in a car. if you are in a moving car, a tree outside will look like it is moving in the opposite direction and it will be doing so at the same speed as the speed of your car and we will always feel like we are at rest
so, we can say that when we are in a car, the objects coming towards us will have our car's velocity added to their velocity, as in the above case, the speed of the tree is 0mph and your speed is v mph, which causes the tree to move back at a velocity of v mph
Now, back to the question. we are in a car moving at a speed of 40 mph and there is a car coming towards us is moving at a speed of 27 mph
If we look at the situation from the eyes of the driver of the car moving at a velocity 40 mph,
he is at rest and the other car is moving at a velocity of (40 + 27) = 67 mph
So, from the frame of reference of the 40mph driver, the other car is moving at 67 mph and the time taken by a car moving at 67 mph to cover 7 miles is the time in which the taxis will meet
Hence, time taken by a 67 mph car to cover 7 miles
time = distance / speed
time = 7 / 67
time = 0.1 hour (approx) or 6 minutes
Therefore, the taxis will meet after 6 minutes
Of the three elevation, -2 feet, -12 feet, and 30 feet, which represents the least number? Which represents the farthest from sea level?
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Answer:
-12 feet represents the least feet and the farthest from sea level.
Step-by-step explanation:
Paul is training for a bike race and is attempting to improve his average speed. With his old trainer, Paul averaged a pace of 20 MPH. With his new trainer, he rode at an average speed of 27 MPH. By what percent did his average speed increase?
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Answer:
5.4%
Hope This Helps!
Please help. This doesnt make sense.
Answers
Answer:
Reflection about the y axis followed by a translation left by 2 units.
Step-by-step explanation:
There is the answer. ^
Write an equation in slope-intercept form for the line that passes through (0, 1) and is perpendicular to the line whose equation is y = 2x? Ay= -2x + 1 B y = 2x + 1 C y = x + 1 Dy=-%2x + 1
Answers
Answer:
y= -1/2 x + 1
Step-by-step explanation:
The line passes through point (0, 1) and is perpendicular to line with equation :
y=2x
Perpendicular lines are those that give -1 when the product of their slopes is calculated.
This means m₁ *m₂= -1
In this case, m₁=2, finding m₂ as;
m₁ * m₂ = -1
2 * m₂ = -1
m₂ = -1/2
Using point (0, 1),m₂ = -1/2, and imaginary line (x, y) then the equation of the line in slope-intercept form y= mx + b will be;
-1/2 = y-1/x-0
-1/2 x = y-1
1-1/2x = y
The equation will be ;
y= -1/2 x + 1
Answer plzzz I don’t understand
Answers
Answer:
Step-by-step explanation:
in a triangle, the sum of all angles is 180 (angle sum theorem). so use the equation 180=50+80+10x. then solve
1. combine like terms
it becomes 180=130+10x
2. subtract 130 from both sides
it becomes 50=10x
3. divide both sides by 10
it becomes 5=x
so, x=5
hope this helped :)
Write 64 as a product of primes.
Use index notation where appropriate.
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Answer:
[tex]{\huge{\pink{\underline{\underline{Question:}}}}}[/tex]
Write 64 as a product of primes.
Use index notation where appropriate.
[tex]{\huge{\pink{\underline{\underline{Solution:}}}}}[/tex]
[tex]Prime\ no.\ is\ 2[/tex]
Factorisation of 64=2×2×2×2×2×2
[tex]{2}^{6} [/tex]
How many 3/4
cups of juice can be poured from 6 cups of juice?
Answers
Answer:8
Step-by-step explanation: 4x6=28
28 divided by 4 = 8
20 points
plz answer soon!
A square on a coordinate plane is translated 9 units down and 1 unit to the right. Which function rule describes
the translation?
O T 1,-9 (x,y)
O T -1,-9 (x,y)
O T -9, 1 (x, y)
O T -9, -1 (x, y)
Answers
Answer: it should be the first one!! :)
Step-by-step explanation:
Answer:its the first one
Step-by-step explanation:did the test
Macie Andersen earns $9.75 an hour working at the local bookstore. Last week she worked 17 hours. This week she worked 25 hours. What was her straight time pay for the two weeks?
Answers
Answer:
$407.50
Step-by-step explanation:
take 9.75 × 17=165.75
take 9.75 × 25=243.75
add 165.75 and 243.75=407.50
turn into dollars $407.50
How could you describe the maximum the LCM between two numbers could be?
Answers
Answer:
the product of the two numbers
Step-by-step explanation:
The LCM of two numbers is their product, divided by their GCF. If their GCF is 1, then the LCM will be their product. That is the most it can be.
__
We assume you're concerned with whole numbers. For rational numbers, the GCF may be a fraction, so the LCM may be larger than the product of the numbers.
LCM(5, 6) = 5·6/GCF(5, 6) = 5·6/1 = 30
LCM(1/2, 3/4) = (1/2)(3/4)/GCF(1/2, 3/4) = (3/8)/(1/4) = 3/2
a seed company has a test plot in which it is testing the germination of a hybrid seed, They plant 50 rows of 40 seeds per row. After a two week period, the researchers count how many seed per row have sprouted. They noted that least number of seeds to germinate was 33 and some rows had all 40 germinate. The germination data is given below in the table. The random variable x represents the number of seed in a row th
Answers
Answer:
Mean =[tex]\sum x P(x) = 36.86[/tex]
Standard deviation =[tex]\sum x^2P(X)=1360.9[/tex]
Step-by-step explanation:
x P(x) [tex]x \times P(x)[/tex] [tex]x^2 \times P(x)[/tex]
33 0.02 0.66 21.78
34 0.06 2.04 69.36
35 0.1 3.5 122.5
36 0.2 7.2 259.2
37 0.24 8.88 328.56
38 0.26 9.88 375.44
39 0.1 3.9 152.1
40 0.02 0.8 32
1 36.86 1360.9
We are supposed to find mean and standard deviation
Mean =[tex]\sum x P(x) = 36.86[/tex]
Standard deviation =[tex]\sum x^2P(X)=1360.9[/tex]
Im not a teacher I want questions to be to answer
Answers
Answer:
Huh now?
Step-by-step explanation:
I am sorry but I do not understand
PLS HELP :(
Solve the inequality and graph the solution on the line provided.
Answers
Answer:
[tex]x\leq -1[/tex]
Step-by-step explanation:
1. [tex]7x\leq 7-14[/tex]
2.[tex]7x\leq -7[/tex]
3. divide both sides by 7
4. [tex]x\leq -1[/tex]
Closed circle on -1 and the line goes to the left
A plane flew at a constant speed and traveled 762762762 miles in 555 hours.
How many miles would the plane travel in 333 hours at the same speed?
Answers
Answer:
457657657.2
Step-by-step explanation:
(762762762/5)*3=457657657.2 miles
The tax on a new pair of headphones is $3.70 and the total cost after tax is $49.95 . What is the pre-tax price of the headphones
Answers
Answer:
the price is 46.25 dollars
Step-by-step explanation:
in which quadrant is the point (4,- 2) located
Answers
Answer:
4
Step-by-step explanation:
According to researchers at Dan Jones & Associates, 1 in every 3 women has been a victim of domestic abuse (Domestic Violence: Incidence and Prevalence Study, Sept.–Dec., 2005). However, many experts on domestic violence believe that the proportion of women who are domestically abused is closer to p = .10. Compare the probability of observing 4 or more abused women in a sample of 15 if p = 1/3 and the probability of observing 4 or more abused women in a sample of 15 if p = .10. The results will lead us to believe that p=1/3 or p=.1? Group of answer choices p=1/3 p=.1
Answers
Answer:
A) 79.08%
B) 5.55%
C)p = 1/3 is more appropriate than p = 0.1
Step-by-step explanation:
This is a binomial probability distribution problem, so we will use the formula;
P(k) = (n!/(k!(n - k)!) × p^(k) × (1 - p)^(n-k)
We want to Compare the probability of observing 4 or more abused women in a sample of 15 if p = 1/3 = 0.3333 and the probability of observing 4 or more abused women in a sample of 15 if p = 0.10
Thus;
P(X ≥ 4) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10) + (P(11) + P(12) + P(13) + P(14) + P(15)
A) Thus at p = 0.3333;
P(4) = (15!/(4!(15 - 4)!) × 0.3333^(4) × (1 - 0.3333)^(15-4) = 0.1949
P(5) = (15!/(5!(15 - 5)!) × 0.3333^(5) × (1 - 0.3333)^(15-5) = 0.2143
Using online binomial probability calculator we can get the remaining values which are;
P(6) = 0.1786
P(7) = 0.1148
P(8) = 0.0574
P(9) = 0.0223
P(10) = 0.0067
P(11) = 0.0015
P(12) = 0.0003
P(13) = 0.0000
P(14) = 0.0000
P(15) = 0.0000
Thus;
P(X ≥ 4) = 0.1949 + 0.2143 + 0.1786 + 0.1148 + 0.0574 + 0.0223 + 0.0067 + 0.0015 + 0.0003 + 0 + 0 + 0 = 0.7908 = 79.08%
B) Now,for p = 0.1 and Using online binomial probability calculator, we have;
P(4) = 0.0428
P(5) = 0.0105
P(6) = 0.0019
P(7) = 0.0003
P(8) = 0.0000
P(9) = 0.0000
P(10) = 0.0000
P(11) = 0.0000
P(12) = 0.0000
P(13) = 0.0000
P(14) = 0.0000
P(15) = 0.0000
P(X ≥ 4) = 0.0428 + 0.0105 + 0.0019 + 0.0003 + 0.0000 + 0.0000 + 0.0000 + 0.0000 + 0.0000 + 0.0000 + 0.0000 + 0.0000 = 0.0555 = 5.55%
C) Comparing both Probabilities, 79.08% is far higher than 5.55%. Thus we can say that p = 1/3 is more appropriate than p = 0.1
find a counterexample for the conjecture: If n is a real number, then -n is a negative
Answers
Answer:
Step-by-step explanation:
-5 is a real number, right ?
- (-5) = 5 is not negative
thanks
EXTRA POINTS AND BRAINLIEST
Answers
Answer:
8+y
Step-by-step explanation:
Sum means that you are adding the constant 8 and the variable y.
Hope this helps!!
Answer:
8 + y
Step-by-step explanation:
"sum" means you are performing addition or adding two quantities/values together
Therefore, the "sum" of "8 and y" is just adding 8 and y together
You just put a plus sign between 8 and y to add them together, so you get 8 + y.
Hope this helps!
:)
Iveta takes out a mortgage of $100,000 to purchase a property. The interest rate is calculated as a simple interest rate of 5% per year. How much interest would Iveta have to pay after six years?
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She would pay $30 000 of interest in 6 years.
To save money you set aside $50. For each following month you set aside 10% more than the previous month.How much money will you save in a year? Explain each step.
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4+ (-3) - 2*(-6)
What is the answer to
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Answer:
13
Step-by-step explanation:
4+(-3)-2*(-6)
4-3-2*-6
1-(-12)
1+12
13
Answer: 13
Step-by-step explanation:
I Had The Same Problem So Try And Its Gonna Be Right.
Simplify the following:
a
2
b
•
b
2
a
2
c
=
a
2
b • b
2
a
2
c =
Answers
Answer:
It is A
Step-by-step explanation:
WHAT 10 x 10 ÷ 5 x 1000 ?
PLS SOMEONE HELP ME!!!!!!!!!!!
Answers
Answer:
20000
Step-by-step explanation:
10 * 10 = 100
100 / 5 = 20
20 * 1000 = 2000
Grady is excavating the foundation of a house. If the hole will be
40 feet long, 24 feet wide, and 4 feet deep, how many cubic feet
of dirt must be removed from the site?
Answers
Answer:
3,840 cubic feet
Step-by-step explanation:
V=LWH
V= 40X24X4
V=3,840 cubic feet
There are five wires which need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attached in any order, and the production manager wishes to determine which order would be fastest for the robot to use. Use the multiplication rule of counting to determine the number of possible sequences of assembly that must be tested. (Hint: There are five choices for the first wire, four for the second wire, three for the third wire, etc.
Answers
Answer:
4
Step-by-step explanation:
44
Given f(x) = -5x - 2, what is the value of f(-3/5)?
Answers
Answer:
1
Step-by-step explanation:
f(-3/5)=-5(-3/5)-2
f(-3/5)=3-2
f(-3/5)= 1
Which is the solution to the equation 0.5X+4.2=5.9? Round to the nearest tenth if necessary.
O 0.9
3.4
5.1
20.2
Answers
Answer:
x = 3.4
Step-by-step explanation:
First start by subtracting 4.2 from both sides and getting .5x = 1.7. Now divide by .5 on both sides. Dividing by .5 is really the same as multiplying by 2, so you get x = 3.4.
Answer:
3.4
Step-by-step explanation:
I did this and got it right