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3 years ago

8

I need help with this please :(

1 answer:

Artist 52 [7]3 years ago

8 0

Answer:

b

Step-by-step explanation:

b= luck

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An environmental engineer is tasked with determining whether a power plant cooling system is heating the water it uses more than

Gemiola [76]

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 $H_o : \mu_1 - \mu_2 = 6$

The alternative hypothesis is $H_a : \mu_1 - \mu_2 \ne 6$

The population mean difference is $\mu_d = 6$

Generally the sample size is n = 15

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

$\= d = 62.57 - 55.97$

=> $d = 6.6$

Generally the standard deviation is mathematically represented as

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

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

=> $s_d = 1.732$

Generally the test statistics is mathematically represented as

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

=> $t = 1.342$

Generally the degree of freedom is mathematically represented as

$df = n - 1$

So

$df = 15 - 2$

=> $df = 14$

Generally the p-value is mathematically represented as

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

Generally from the t -distribution table the probability of 1.342 at a degree of freedom of $df = 28$ is

$P(t > 1.342 ) = 0.10047$

So

$p-value = 2 * 0.10047$

=> $p-value = 0.201$

Generally from the value obtained we see that $p-value > \alpha$ 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

7 0

3 years ago