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: 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?

Answer 1

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?

Answer:

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 $X_1, ......, X_6$ as the cost of production using the new Process

Let's also take $Y_1, ....,Y_6$ as cost of production using the old process.

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

Therefore we have:

For null hypothesis

$H_0 = U_x - U_y ≥ 0$

For alternative hypothesis

$H_0 = U_x - U_y < 0$

Therefore for the mean we have:

Old mean cost=

$Y = \frac{50+54+59+56+50+58}{6} = 54.5$

New mean cost=

$X = \frac{51+52+55+53+54+53}{6} = 53$

53 -54.5 = -1.5

For null;

$H_0 = -1.5 ≤ 0$

For alternate

$H_1 = -1.5 > 0$

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.