So now we have to collect 30 observations because we would

like to test our null hypothesis with such observation of cans.

So let's suppose we randomly pick in this factory 30 cans and measure the content.

In the following table you see the content of 30 cans.

So some of them are both 32 centiliters and some of them are below 32 centiliters.

We can use this data to first of all compute the mean of the sample.

And the mean of the sample is 32.5 centiliters if you compute the mean correctly.

Another thing we have to do is to compute

the variance or the standard deviation of this sample.

In the same manner as we've done it before,

if you compute the sample variance or the sample standard deviation,

the standard deviation will be 0.128.

The next step will be to construct the statistics that will

determine whether we reject or whether we accept the null hypothesis.

The way to construct the test for hypothesis will

be to construct a z value which will be equal to,

our estimator, point estimate,

which is in our case the mean of sample x upper bar,

minus the m which is the hypothesis itself that we propose,

over sample variance of sample standard deviation divided by

the square root of n. You already see some similarities

between this and the intervals, confidence intervals.

So the confidence interval for the sake of this example, if you remember,

will be m equal to x upper bar plus minus z that corresponds to

95 percent confidence times sigma over square root of n. In the previous case,

the sigma was known because we were given that.

In that case, it is not known and therefore,

we have to use an estimate of that by using

the information that was provided in the sample.

You see the similarity between this and this is quite striking.

Now, moving to the next stage.

We mentioned that the sample mean is equal to the 32.05 centiliters.

We know what m is, is 32 centiliters.

We know that this value,

the standard deviation of the sample is equal to 0.125.

And we know the sample size is 30.

If we do the calculation correctly,

the z value where we have is 2.139,

which lies if we take

this distribution in this region to 2.139.

Because it is in the rejection area,

we will have to say that our null hypothesis is rejected,

and therefore we accept the alternative hypothesis.

In other words we say,

that our null hypothesis is that average of cans is

32 centiliters is incorrect with 95 percent confidence,

and the alternative is the correct.

But it's very important to understand what alternative means.

It means that we do not know whether it is greater or less.

It can be either.