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 HW_PTA 243.csv.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?
A) The cooling system changes the temperature of the water by an amount different than 6 degrees.
B) The cooling system changes the temperature of the water by 6 degrees.

Complete Question

The complete question is shown on the first , second and third uploaded image

Answer:

A

 The correct option is A

B

  The correct option is H

Step-by-step explanation:

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]      

The population mean difference is  [tex]\mu_d  =  6[/tex]

Generally the sample size is  n =  15      

Generally the sample mean for 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 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 sample mean difference is mathematically represented as

   [tex]\= d = 62.57 - 55.97[/tex]

=>[tex]d = 6.6[/tex]

Generally the standard deviation is mathematically represented as

       [tex]s_d  =  \sqrt{\frac{ \sum [d_1 - \= d]^2}{n-1} }[/tex]

=>    [tex]s_d  =  \sqrt{\frac{ [ [57.6 -65.1]- 6.6]^2 +[68.9 -74.4]- 6.6]^2+\cdots +   [60.4 -67.3]- 6.6]^2}{15-1} }[/tex]

=>     [tex]s_d  = 1.732 [/tex]

Generally the test statistics is mathematically represented as

      [tex]t =  \frac{6.6  - 6 }{\frac{1.732}{\sqrt{15} } }[/tex]

=>   [tex]t = 1.342 [/tex]

Generally the degree of freedom is mathematically represented as

    [tex]df  = n -  1[/tex]

So

      [tex]df  =  15  -  2[/tex]

=>    [tex]df  =  14[/tex]

Generally the p-value  is mathematically represented as

     [tex]p-value  = 2 *  P(t >  1.342 )[/tex]

Generally from the t -distribution table the probability of 1.342 at a degree of freedom of  [tex]df  =  28[/tex] is  

       [tex]P(t >  1.342 ) = 0.10047[/tex]

So

     [tex]p-value  = 2 * 0.10047[/tex]

=>   [tex]p-value  = 0.201[/tex]

Generally from the value  obtained we see that [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

The angle measures of triangle QRS are given:

The measure of angle Q is (5x−15)°.
The measure of angle R is 75°.
The measure of angle S is (3x)°.
What is the value of x?

Factorise fully
40-10g

Please do quick, will mark brainiest!!​

Simplest form of 8/36

Convert 139 pounds to kilograms
Round answer to the nearest tenth.

Conversion table:
1 kilogram = 2.205 pounds

What is the value of j

Use a system of linear equations with two variables and two equations to solve.

175 students enrolled in a freshman-level chemistry class. By the end of the semester, 4 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed.

2/15 = h/125 need a step by step please

бx + 8 = 50
I need that answer

Simplify and find the value for 1) x = -1, y = 1 and z = 2 (x – 2y) (3x2 + 4xy – y 2 )

Quadrilateral GHJK has vertices G(2, 3), H(8, 2), J(6, 8), and K(3, 6). It is transformed according to the rule T(–4, –5).

What are the coordinates of G”?

(–7, 3)
(–2, 2)
(–1, –7)
(2, –2)

Show that each conjecture is false by finding a counterexample.


1.For any integer n, n3 > 0.


2. Each angle in a right triangle has a different measure.


3.For many years in the U.S, each bank printed its own currency. The variety of different bills led to widespread counterfeiting. By the time of the Civil War, a significant fraction of the currency in circulation was counterfeit. If one soldier had 48 bills, 16 of which were counterfeit, and another soldier had 39 bills, 13 of which were counterfeit, make a conjecture about what fraction of bills were counterfeit at the time of the Civil War.

there is a box that contains a $50 bill, two $20 bills, three $10 bills and four $1 bills. If a bill is picked at random, what is the expected value?

2/3 divided by ? = 6/8 ASAP

11. Factor for

12 – 8.1 + 16​

To win a trivia game you must score 90 points each correct answer is worth 1 3/4 points, each incorrect point is worth -1/4 points if he gets 58 questions correct and 22 questions incorrect, what is his score?

The difference of two integers is 1. The product of the integers is 30. What
are the integers?

Need help ASAP with my math

Tabithas living room is rectangle that measures 19 3/4ft by 12ft find the perimeter and the area of the room

A florist sold 45 flowers in a day and 60 flowers on the next day. If p is the percent increase in the number of flowers sold, which proportion can be used to calculate p?

1) Suppose you buy a laptop costing $1850 at a store charging 12% add-on interest, and you make a $500 down payment.

bob is on his way home in his car. he has driven 30 miles so far, which is three-fifths of the way home. what is the total length of his drive?​

(-8) X 2/3 i NEED the answer help me

Pls I need help ASAP

Follow the steps to find the value of x
1.Addition property of equality.
1/5(x)-2/3=4/3
1/5(x)-2/3+2/3=4/3+2/3
2.Multiplicative property if equality.
1/5(x)5/1=6/3(5/1)
The solution is x=
​

What is the sign of the product (3)(−25)(7)(−24)?

A. Positive, because the products (3)(−25) and (7)(−24) are negative, and the product of two negative numbers is positive
B. Positive, because the products (3)(−25) and (7)(−24) are positive, and the product of two positive numbers is positive
C. Negative, because the products (3)(−25) and (7)(−24) are negative, and the product of two negative numbers is negative
D. Negative, because the products (3)(−25) and (7)(−24) are positive, and the product of two positive numbers is negative

Megan had $235.17 in her bank account. She withdrew $77.98 from the account to spend
on clothing. How much money does she have left in her bank account now?

|3d-3n|-4 if n=2 and d=3

Solve for X please :(( Will give brainliest.

ax+6=15 a is a negative, what must be true about x?

x+y=k
x-y=k
The solution of the system shown is
O (OK)
O (0,0)
O (k, O)