Now I will explain you this critical value method by taking two more examples.
Where we will see that there if there is one tailed test, then what will be the difference in the value or if I have normally such a value, where if we change the alfa then in which ways there will be a change in our value.
So, the second example is somewhat in this way, there is one manufacturer, okay.
He said that whatever product he has its average life cycle is 36 months, which means any manufacturer is claiming that if you take this product of mine then it will definitely last for three years.
So, the average lifecycle of the product that he has said is 36 months.
Now, suppose any auditor comes, which means such a person who is doing the sampling the survey.
What he did is, he randomly picked any 49 samples of his products and he calculated its sample mean and standard deviation, after calculating sample mean, lets say X bar that came was 34.5 months and standard deviation S comes to four months.
So, in this situation if you will see.
First of all it should come to your mind that by using critical value method, we can find out that whether my population mean is 36 months or not.
In this situation our null hypothesis would be that mew is equal to 36 months.
An alternate hypothesis will be mew is not equal to 36 months.
So, since it is a two tailed test, we have seen that why it is a two tailed test? Why? Because my mew is equal to 36 months, since we don't have a right and left tail, this distribution will lie on both the sides.
If in two tailed test I will take alpha’s value as 0.03.
Since this is a two tailed test, then my critical region’s value would be divided by 2, which means if 0.03 is my alpha, then to calculate UCV, we will use 0.03 divided by 2.
Now to calculate the cumulative probability, what will be the formula, 1 minus 0.03 divided by 2.
So, in this particular case, my UCV’s value, which means such a value corresponding to which we found ZC, that comes to 0.9850.
Now corresponding to 0.9850 Whatever is my Z score, that we will find out through the Z table.
Because of that my Z score that comes, that is 2.17.
How did that come? If you see in the horizontal way, then its value is 2.1.
And if you see in vertical then it is 0.07 which means that my Z score came to 2.17.
Corresponding to that I calculated LCV and UCV.
I calculated LCV, so its value came to 34.76 and I calculated UCV, its value came to 37.24.
So, what do you remember? Whatever was my sample mean, which we were assuming was 34.5 months and your range that came, that was from 34.76 to 37.24.
Which means that our sample mean is lying on a critical region.
Now if the sample mean lies in the critical region.
So, we can simply reject our null hypothesis.
So, this was my example.
In this way we will see the third example, in which we will take the case of AC manufacture.
What had we seen in the first example? That whichever is my monthly mean, which is my monthly sales, will it be equivalent to 350 or not.
Since we have to perform one tailed test then we will assume that our average demand of AC units, will be at the most 350 units.
Which means my null hypothesis will change now.
Rather then, mew is equal to 350 units, now my null hypothesis will be mu plus less than is equal to 350 units.
The responding to that my alternate hypothesis which will be there, which means x one would be mew is greater than 350 units in this situation.
This will perform mew less than is equal to 350 units.
Corresponding to it whichever will be my alternate hypothesis, which means h1, it will be mew is greater than 350 units.
In this situation it will perform one tailed test.
If we specifically see one tailed test, then this will be upper tailed test.
Why? Because mew’s value in alternate hypothesis I greater than 350.
Greater means my distribution will lie on the right-hand side and this would be my upper tailed test.
One important thing or one important difference which we have to keep in mind is that when we use two tailed test, then we divide the alpha value by 2 but if we are using one tailed test, which means we are using upper tailed or lower tailed test then we will directly use any value of alpha, that is not divided by 2.
So, let's consider that my alpha is 0.05, which means we are assuming that in my test.
There is a chance of 5% error.
How will we calculate UCB corresponding to that? Simply 1-0.05, then my value comes to 0.9500.
Corresponding to 0.9500 now we will calculate one Z score.
But if you will see carefully for 0.9500, there is no value in Z table.
So, what we will simply do is, whatever values are there before and after it, we will take those two and calculate its mean, which means 0.9495 and 0.9505 responding whichever values comes, which is 1.64 and 1.65.
I will take them both and calculate its mean and whichever value that will come, that will be my Z score.
So, my Z score in this particular case comes to 1.645.
Now, one important thing which we have to remember in one tailed test, since we are calculating UCV over here, so we will not calculate at LCV here.
Why? Because if we are performing two tailed tests, so we wanted a particular interval, that what is my lower critical value and what is the upper critical value? But if you're using UCV, you're using one upper tailed test.
So simple, corresponding to UCV value we can tell that my value lies in the acceptance region or it is lies in the critical region.
So, in UCV I have put my values, which means mew plus Z C’s value, which is 1.645 multiplied by sigma upon under root n.
With that my UCV’s value comes to 374.67.
Now if you will see that the mean that we have calculated that was 370.16, which means that is less than UCV.
So, this means that my sample means lies in the acceptance region.
And we can say that we are not rejecting our null hypothesis.
So, this means that my sample mean lies in the acceptance region and we can say that we cannot reject our null hypothesis, so this means that we fail to reject the null hypothesis.
In this way, in different scenarios, by using our critical method, we can prove our hypothesis.
We will see once, a small summary of whichever methods we have applied.
What exactly are the steps that we have to follow if we have to use critical value method.
very first work will be to see what is ZC.
Corresponding to that ZC, we will find our Z score, which will help us in finding UCV and LCV.
When you will find UCV and LCV, corresponding to that you will make your decision that my sample mean is lying in the acceptance region or my sample mean is lying in the critical region.
And your simple decision will be in this way.
If sample mean lies in acceptance region, then we fail to reject the null hypothesis and if the sample mean lies in the critical region, then we will simply reject our null hypothesis.
So, in this module, we covered critical value method.
If you have any comments or questions related to this course then you can click on the discussion button below this video and you can post them over there.
In this way, you can connect with other learners like you and you can discuss with them.
This course is really nice, just have one question in empirical rule explanation , SD deviation example trainer is saying mean however mean (20+30+40+50+60+70/6) value is different kindly confirm than