So, we saw through the examples, how do we use p value method, but in p value method generally a lot of people get confused that if my distribution is on the right side then I should call this p value or if my distribution is on the left side then what would be my P value.
So, let's understand this with two scenarios in a very simple way.
Imagine that I have one right side distribution, which means my Z source code is positive and it lies on the right side.
Z scores value, let's assume here is plus 3.02.
Corresponding to Z score whichever value that you calculate with your Z table, what is that called? Cumulative probability.
So, here my cumulative probability came as 0.9987.
Corresponding to that value, if we have to find p value, since it lies on the right-hand side.
This probability of one tailed test is 1- 0.9987 which means it will be 0.0013.
But if it is a two tailed test, then we will multiply it with two, which means whatever value we have got, we will simply multiply it with two.
But if the second situation is that my Z score is negative, which means by distribution lines on the left, in that situation we will use the left Z table and find our cumulative probability.
If suppose my Z score is -3.02.
Then I will find a cumulative probability corresponding to it, which comes to 0.013.
In the case of one tailed test, whichever is your cumulative probability, directly that will become your p value.
We have to pay attention here, if you will see this curve where my Z’s value is positive.
So, whatever is on my left side, that would be my cumulative probability.
If we will subtract it from 1, that would be my P value.
But if we assume that my Z’s value lies on the left.
If it is lying on the left whatever is my cumulative probability that will directly become my p value.
So, this is a very important topic, which you have to keep in mind, there is a lot of confusion that what is the correct p value, what is wrong or what is right, when I have to subtract it from 1.
When I have to multiply it by 2.
So, all these situations and confusions, you can clear them all here through both these scenarios.
Normally, for 1 tailed value my p’s value will be that.
For 2 tail test we will multiply it by 2.
Now we will see how we calculated all the p value.
What is the confusion, that we have already seen? Let’s see once, the two examples that we had learned in critical value method, how they come to use in the practical implementation.
It’s the same example that the manufacturer’s claim is that till 3 years my average product will work, which means the average lifecycle of their product is 36 months.
In that auditor has taken n=49 unit’s sample.
It calculated its average life, which means the sample mean.
Which comes out as 34.5 months.
Standard deviation is 4 months.
In this situation null hypothesis will be the same, 36 months.
Alternate hypothesis would be mew is not equal to 36 months.
What is the first thing that we do? We calculate a Z score of our sample mean.
Sample mean means our 34.5 value which is there, we will calculate a Z score corresponding to it.
So, when we put its value in the formula.
Then that comes to -2.62.
If we pay attention, my Z score lies on the left side.
Which means whichever will be my cumulative corresponding probability, that will directly be my p value, which means since it is on the left side, this distribution.
We will simply find its value which comes out as 0.0044.
Like you can see in the graph or this table.
Horizontal side of -2.6, vertical side of 0.02, whatever is the value will be my Z value.
Why? Because they were on the left-hand side, my simply p value was as it is.
But bear in mind since it is a two tailed test, we will multiply it by 2.
Now we have taken one significance level.
Let's say we are testing it for 3% significance level? So, for 3% my 0.0088 value that is there, that is less.
That means that my value has started to lie in the critical region.
So, we can simply say that my null hypothesis can be rejected.
And the average lifecycle of he product is not 36 months.
So, in this way, we can very easily use P value method and perform out analysis or hypothesis.
Now I am taking one more example, the same AC sales one.
The only thing in this test is how do we perform in 1 tailed test, to see that.
The example is the same.
Here I have the null hypothesis, that mew is less than equal to 350 units.
In the last example mew was equal to 350 units.
Here we are seeing the almost condition so that we can do one tailed analysis.
Simply I calculated Z score by putting the value in the formula.
This time my Z score comes as positive 1.344.
Positive means that our distribution lies on the right, because of it laying on the right, whatever is my P value that will be 1 minus cumulative probability.
Did you see, what we had read at that time that this confusion will not happen.
How is the system of right and left.
That if you easily keep in mind then it will be very easy for you, in which ways we will put the values and it will give us the result instantly.
So, in the upper tailed test situation, normally we don’t have to multiply it by 2.
Whatever is the Z’s value that we will get in this table, that we directly subtracted by one.
That will become directly my p value.
My p value come to 0.895.
Now if I test it for 5% significance level.
If the p value is greater than significance level.
Now if simply p value is greater.
Then it means that we cannot reject a null hypothesis.
And we came to a conclusion that this is our final analysis.
In this way we do our P value method and it is used a lot in the industry.
So, once we will see its summary.
After creating null and alternate hypothesis.
What are the steps that we follow and in which ways we form decision.
We simply calculate the Z score, in the first step of sample mean.
Normally, on the basis of the Z score formula.
On that basis, we will calculate a P value, which is cumulative probability based on left or right distribution, whatever it may be.
In the third step, we will simply see, if it is a two-tailed test, we will multiply it by 2 and if it is a one-tailed test, so normally whatever is my value that becomes my p value.
Simply if you have alpha, then corresponding to that we compare our p value.
If my p value is greater than significance level then we fail to reject the null hypothesis.
If my p value is less than significance level then we reject the null hypothesis.
In this module we have covered that how P value method is used.
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