[MUSIC]
In traditional hypothesis testing,
one has the option to perform z-test or a t-test, and the question is,
under what circumstances should one perform a z-test or a t-test?
Well, the answer is rather simple, if one is aware of the populations
standard deviation or variance, we use the z-test.
And that is when we are comparing the sample mean to a hypothetical or
a population mean.
And if the population standard deviation is not known and
we're comparing the sample mean against the population mean within unknown
standard deviation, then we use the t-test.
Now there are four scenarios in which we perform these tests.
First scenario is where we are comparing a sample mean to a population
mean and the population standard deviation is known,
in that particular case, we use a z-test.
And in cases where we are comparing a sample mean to a population mean with
an unknown standard deviation, we use the t-test.
Now this I covered earlier in the last slide.
The new thing here is that when we compare the means of two independent samples, that
is comparing the means of two independent samples with unequal variances.
If we are faced with this kind of a question, we use a t-test.
Again, if we are comparing the means of two independent samples with
equal variances, we still use a t-test.
The underlying theory is that when you're using a z-test,
you're basing your results on normal distribution, and
when you are deploying t-test, you're basing your results on t-distribution.
And the process of hypothesis testing could be
made rather simple by looking at these thresholds.
If you are comparing the means and
in the particular case you are looking at the null being that the two
averages are the same against two averages not being the same.
Then you're using a two-tailed test, and in that particular case you're looking for
a t-statistic or z-statistics of 1.96, the absolute value of 1.96.
If that were to be the case, you reject the null hypothesis.
That is, you're conducting a two-tailed test.
You can be using normal distribution or a t-distribution, and
you get the calculated z or t-statistics of greater than absolute value of 1.96.
And the expected p-value,
the probability of that happening would be less than 0.05 and you reject the null.
The null being that the two means are equal.
In the case of one-tailed test, where you're testing whether the mean or
average of one entity is greater or less than the other,
here the absolute value for z or t-statistic is 1.64, and
the probability would still be less than 0.05.
If that were to be the case, you reject the null.
If the calculated value for z or t-statistic is less than 1.96, you fail
to reject the null hypothesis, and the null being the two averages are the same.
In case of a one-tailed test and the calculated value for z or
t-statistic is less than 1.64, you fail to reject the the null and
the null could be that one value or the average is less than or
equal to the other or is greater than the other.