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 [tex] X_1, ......, X_6 [/tex] as the cost of production using the new Process
Let's also take [tex] Y_1, ....,Y_6 [/tex] as cost of production using the old process.
Therefore, [tex] U_x and U_y [/tex] will be the mean cost of production of the new process and old process respectively.
Therefore we have:
For null hypothesis
[tex] H_0 = U_x - U_y ≥ 0 [/tex]
For alternative hypothesis
[tex] H_0 = U_x - U_y < 0 [/tex]
Therefore for the mean we have:
Old mean cost=
[tex] Y = \frac{50+54+59+56+50+58}{6} = 54.5 [/tex]
New mean cost=
[tex] X = \frac{51+52+55+53+54+53}{6} = 53 [/tex]
53 -54.5 = -1.5
For null;
[tex] H_0 = -1.5 ≤ 0 [/tex]
For alternate
[tex] H_1 = -1.5 > 0[/tex]
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.
