BRAINLIEST AND 21 POINTS NEED HELP ASAP

Paired t-test Application (Part 1)An environmental engineer is tasked with determining whether a power plant cooling system is h

qaws [65]

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

$\= x _1 = \frac{\sum x_i}{n}$

$\= x _1 = \frac{57.6 + 68.9 \cdots +60.4 }{15}$

$\= x _1 = 62.57$

Generally the sample mean for the output temperature is mathematically represented as

$\= x _2 = \frac{\sum x_i}{n}$

$\= x _2 = \frac{65.1 + 74.4 \cdots +67.3 }{15}$

$\= x _2 = 55.97$

Generally the difference between the mean of the input temperature and that of the output temperature is

$d = \= x_1 - \= x_2$

=> $d = 62.57 - 55.97$

=> $d = 6.6$

Generally the standard deviation of the difference between the input temperature and the output temperature is mathematically represented as

$s_d = \sqrt {\frac{1}{n-1 } \sum [d_i - d]^2}$

=> $s_d = \sqrt{\frac{[(57.6 - 65.1) - 6.6]^2+[(68.9 - 74.4) - 6.6]^2+ \cdots +[(68.1 - 74.7) - 6.6]^2 }{15-1} }$

=> $s_d = 1.732$

The null hypothesis is $H_o : \mu_1 -\mu_2 = 6$

The alternative hypothesis is $H_a : \mu _1 - \mu_2\ne 6$

Generally the test statistics is mathematically represented as

$t = \frac{d - 6}{ \frac{s_d}{ \sqrt{n} } }$

$t = \frac{6.6- 6}{ \frac{1.732}{ \sqrt{15} } }$

$t = 1.342$

Generally the p-value is mathematically represented as

$p-value = 2 * P(t > 1.342)$

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

$P(t > 1.342) = t_{1.342 , 14} = 0.100478$

So

$p-value = 2 * 0.100478)$

$p-value = 0.201$

From the values obtained we see that the $p-value > \alpha$ 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.

5 0

4 years ago

How high would a two story building be if each story was 15ft.? What about a 10-story building? What about a 30-story building

Serhud [2]

This is a very simple question, however having all the words are pretty confusing, right? Don't worry I am going to break it down. First thing you want to do is forget about how many stories are how many feet, because you are trying to find that but are probably getting very confused. So write down that the word EACH= 1-story, Then have 1-story= 15ft. so basically you add 15 to every story. 1=15, 2=30, use this to find the answers 15x= ft---> 15(10)=150ft---> do the last one. If you anymore questions I will break it down further, I used to have a hard time with these.

5 0

3 years ago

Find the polygon that is similar to ABCD.

Yuri [45]

I think the answer should be B

5 0

3 years ago

Read 2 more answers

Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive

Elena L [17]

Answer:

Constructive Proof

Step-by-step explanation:

Let x be a positive integer

x must be equal to sum of all positive integers exceeding it

i.e.

x = x + (x - 1) + ( x - 2) + ......... + 2 + 1

Equivalently,

x = ∑i (where i = 1 to x)

The property finite sum;

∑i (i = 1 to x) = x(x + 1)/2

So,

x = x(x + 1)/2 ------- Multiply both sides by 2

2 * x = 2 * x(x + 1)/2

2x = x(x + 1)

2x = x² + x ------- subtract 2x from both sides

2x - 2x = x² + x - 2x

0 = x² + x - 2x ----- Rearrange

x² + x - 2x = 0

x² - x = 0 ------ Factorise

x(x - 1) = 0

So,

x = 0 or x - 1 = 0

x = 0 or x = 1 + 0

x = 0 or x = 1

But x ≠ 0

So, x = 1

The statement is only true for x = 1

This makes sense because 1 is the only positive integer not exceeding 1

1 = 1

It is a Constructive Proof

A proof is constructive when we find an element for which the statement is true.

8 0

3 years ago

Combine like terms in the expression below. 5c + 6 + 8c - 2 Plz help

Eva8 [605]

Answer:
13c+6-2

Explanation:
You combine the amount of cs with each other.

8 0

3 years ago