In this session, we will discuss about confidence in those.
A confidence interval refers to the probability that a population barometer will fall between two sets
of values for a certain proportion of times.
Confidence intervals measure the degree of uncertainty and also in the sampling method.
Now, let us look at this.
Neighbors say they have this particular data.
And we want to debate that there is a particular value see 25.
And we want to find out if the 25 value actually falls in this normal.
So confident Sandoval will be able to provide us a probability that there is a little if for people
are saying or 90 percent or 100 percent chance that 20 will be falling in this good or twenty five will
be falling in this cycle.
So this is what confidence in Bellevue's.
So we will get the probability like this is the probability that this value will fall in the Gulf.
And what is the limit around which it will be present?
So let us say it will give an interval that the value will be present between 20 and 24.
Or let us see the value will be preserved between 18 and 22 from our previous example.
Like the meaning of this particular distribution will be from 18 to 22 now, the confidence associated
will be a different value.
So this is what the confidence interval is.
Confidence interval is basically a value or range which provides a probability barometer that something
will fall between two sets of values.
Now, some properties of this is that it will be symmetric about the meaning of data.
Any convincing interval will be symmetric about the meaning of the data.
Confidence in the will can have differing degrees of confidence, such as 60 percent confidence, 80
percent confidence.
Ninety nine percent confidence.
This forcing the confidence means that out of a hundred samples taken.
60 samples will have this particular mean value.
We have an arrest we are not sure of.
Similarly, 99 percent confidence means that out of a hundred samples, the mean value will be X and
that will be in 99 of the samples out of hundreds.
Now, greater the sample size, smaller the confidence interval.
So when we are taking let's say we have 100 population values, our population has hundred values,
and I'm taking a sample of, say, only 20 values.
So their confidence interval will be larger.
Because I am not sure if I'm taking only 20 values as a sample, then the window of the confidence interval
will be larger because when my sample sizes one, I will not be able to be sure about that.
What will be the range of the meat?
So if I will, I have only 20 values.
I will not be sure that the machine will be exactly 20 or it will be 18 or it will be 16.
I might say that if there are only 20 values which I have got in the sample and the population sizes.
So maybe.
The mean good to be around see 30 to 60, I can say something like that, but when I have around 70
values in my sample and then I have the mean of my sample as 50, then I can see with more confidence
that the value of the machine will be somewhat around 50.
So let us see that it will be around forty five to fifty five.
I can be more precise.
I can be more sure because my population size is somewhat near to the sample size and then the sample
size will be exactly the same as the population size.
Then I will be 100 percent sure what my means.
So the confidence interval will be more moyet.
So this is what the states, the greater the sample size, the smaller the confidence interval that
is more accurate determination of the population mean from the sample mean different sample means will
have some different confidence in votes.
So if they have one sample, it has different of one sample mean and there is another sample which has
another sample mean.
So the confidence interval will also be different for both of these.
Now.
Here, one minus Alpha gives the probability that the true value falls into the calculated interval.
OK, so we can also give a confidence level in person.
So what will be the confidence level?
Let's say we have a confidence level of 90 percent, 95 percent or 99 percent legacy.
I work in an organization and they want me to provide me that.
There is I want I have to give them that.
I am 95 percent sure what should be the mean of the something I need to provide this particular data
that what should be the mean of a particular population based on the sample which I have and I want
I have to be 95 percent sure, then what I will do is I will be considering the.
Alpha value as ninety five percent.
So what will I have, one minus Alpha as five percent.
So here's my alpha value will be five percent, which is zero point zero five.
So I will be calculating my alpha value, my Z barometer, the critical region, whatever values I will
be calculating for this confidence interval on the basis of alpha value, considering at zero point
zero five.
This will be my criteria now how we use this criteria.
We will learn about it, but for now, just try to understand that when I want to have a confidence
interval, when I want to determine something, when I want to determine a population barometer, I
have to provide my insight on some confidence level.
I have to provide the confidence level.
So let us see.
My organization wants me to be 95 percent confident.
So in that case, my confidence interval would have to be 95 percent.
So my one minus alpha value one will be the probability eight out of a hundred percent.
I want to be 95 percent sure.
So the confidence interval, the range of the interval has to be five percent.
And what is five percent?
Five percent is equal to zero point zero five.
So then I'm looking at only one direction, it will be zero point zero one zero point zero two five
days, we will look at it for now.
You can ignore this entire thing.
Just remember that my alpha level will be zero point zero for.
So we can give the confidence level in person.
So this is a confidence interval, the most in the confidence interval at informal point, that's going
to be the margin of error.
So we will have some value.
We will have some mean value, which we will calculate.
And based on this value, we will give up value in the will value a margin value that I am sure that
the mean for me is 50.
So from this mean 50, the confidence in those states that there can be an error of five in this.
So when I say five, so it will be my mean value, minus five, I mean value plus five, anything would
be of value.
So the value could be either 45 or 50.
It could be between forty five and fifty five.
For me the value is fifty, but there is a margin of error of five.
So the value can range from 45 to 50.
This is what how a confidence interval would be stupid.
And this I will be determining on the basis of the confidence interval how we going to do this while
we're doing this, we will look at it in something.
Now.
We will be having certain range of values.
So the values will be now this interval, the confidence interval, which we will be having.
So my task is to find out the mean value value I have to find out mean of my population and the mean
of the population will be the central value of my flock.
Now, I have one son, Bill, and I have a mean value now, the exact value of the population mean could
be a little bit higher also and a little bit towards the right side.
Also, either the value will be towards left, either the value will be towards right.
So it will be either plus two, minus two or it will be plus three, minus three and accordingly.
OK, so it will be symmetric in nature.
Now, the confidence level will be one minus Alpha, which we have already discussed.
Now the value of the range will be.
It'll be this value will be it, and this value will be we are seeing the value will be between 45 and
55, so forty five will be it and 55.
Will we be with the meanest 50?
Now, how will we find out the probability?
The probability of success, what we are seeing here is now we are seeing that this is the change we
provide, the mean value we provide, the minimum value and the maximum value we provide the margin
value also that this is the margin value.
It will be either a less minus five or less like this.
It will be 50 minus five.
That is 40 or 50 plus five, that is.
Fifty eight.
So when I have a percentage in it, I have an interval of.
Five percent.
When I have an interval of five percent, when I have an interval of ninety five percent pure.
This is one minus Alpha.
What was my confidence in the.
My confidence interval was like us in 95, it's not dead in this gives Nickerson, in this case, we
have confidence in the will of 90 percent.
OK, and now in that scenario, we are considering the confidence in the will of nine people.
So what will this be?
This will be one this will be 90 percent.
So the 90 percent of data will be 90 percent of the values will be present under this plot.
Ninety percent of the values will be present, this blog.
So the value which we are looking at.
Will be under this 90 percent I have I am going to be 90 percent sure that the value is lying between
this.
Ninety percent of the area of the plot I'm covering and I'm seeing that the confidence is 90 percent.
So what am I losing at?
I am losing Aftenposten.
I am not confident by that.
What am I not confident of it?
I am not confident with the enforcement of that.
So I am not confident that enforcing.
So this is 90 percent and this is a joke, this is a symmetric distribution, so the 10 percent will
be divided between this part and this part.
So this idea will again have five percent and this CGI will also have five percent.
So that is why we have this.
AlphaBeta.
Zero point zero.
So this is all we can find out.
The confidence interval.
So how will we find out?
Confidence interval now.
Think in themselves, they think in terms of how we would calculate things, if we have certain value
of the sampling distribution, we had some distribution, we had a sample here and in the sample we
had some distribution of data.
We said the values are ranging from one, two hundred and from these values ranging from one 200.
We have 50 here, which is the mean value.
And this is the distribution of the data and from this distribution of data, we want to find out what
should be the population me now my population has a lot more values presently, say a thousand or two
thousand or five thousand views.
So I'm not sure if this 50 is actually the mean of my population.
So that is why to my organization or to my manager I want to provide the means should be something between
some range.
The is between the range and the.
But I am not sure what envy's.
So my manager asked me that.
What is the percentage, what is how much confidence.
What.
So give me some confidence level that you are ninety.
Something like you, you will be 90 percent sure that between which the value should be changing so
you give them the value should be ranging between this and this, which is 90 percent of my data.
Which is 90 percent of my data, so it will be changing between this area.
Now, this area is owned by me, so that is why I will be left with five percent here and five percent
here.
So this much complete area will be 90 percent.
So if I give this range, so 90 percent of my data will be covered inside this.
So I can say I'm 90 percent sure that the machine will be lying within this.
So now our focus is to find out what does this value and what does this value and how do we find that
out?
We we find that out based on the z value which we have used.
And how do we find the Z value?
The Z value is followed based on this X.
X minus mu divided by.
Sigma.
So based on that, I can find out the value and now we don't have the X value here, we don't have the
X value, but we know the Z school what what the Z score should be.
So we will find out the Z score.
And based on the score, we can find out what the value should be and hence we will be able to find
the confidence and now we will see how they do that.
But they know this is just theoretically how we will be finding out the confidence in the will and the
confidence level.
This is one example which we will be discussing about this.
In the next session.