It is thought that a new process for producing a certain chemical may be cheaper than the currently used process. Eachprocess was run 6 times, and the cost of producing 100 L of the chemical was determined each time. The results, indollars, were as follows:New Process: SI 52 55 53 54 53Old Process: 50 54 59 56 50 58Can you conclude that the mean cost of the new method is less than that of the old method?

Complete question:

It is thought that a new process for producing a certain chemical may be cheaper than the currently used process. Eachprocess was run 6 times, and the cost of producing 100 L of the chemical was determined each time. The results, indollars, were as follows:

New Process: 5I 52 55 53 54 53

Old Process: 50 54 59 56 50 58

Can you conclude that the mean cost of the new method is less than that of the old method?

Yes, we can categorically say that the average mean cost of the new is lower than the old process, even if that is the case.

Step-by-step explanation:

Let's take as the cost of production using the new Process

Let's also take as cost of production using the old process.

Therefore, will be the mean cost of production of the new process and old process respectively.

Therefore we have:

For null hypothesis

For alternative hypothesis

Therefore for the mean we have:

Old mean cost=

New mean cost=

53 -54.5 = -1.5

For null;

For alternate

Since our value -1.5 is less than -0.05, we reject the null hypothesis.

Therefore, since alternative hypothesis is the case, we conclude that the average mean cost of the new is lower than the old process.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: