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[MUSIC]

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In traditional hypothesis testing,

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one has the option to perform z-test or
a t-test, and the question is,

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under what circumstances should
one perform a z-test or a t-test?

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Well, the answer is rather simple,
if one is aware of the populations

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standard deviation or
variance, we use the z-test.

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And that is when we are comparing
the sample mean to a hypothetical or

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a population mean.

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And if the population standard
deviation is not known and

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we're comparing the sample mean against
the population mean within unknown

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standard deviation,
then we use the t-test.

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Now there are four scenarios in
which we perform these tests.

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First scenario is where we are comparing
a sample mean to a population

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mean and the population
standard deviation is known,

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in that particular case, we use a z-test.

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And in cases where we are comparing
a sample mean to a population mean with

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an unknown standard deviation,
we use the t-test.

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Now this I covered earlier
in the last slide.

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The new thing here is that when we compare
the means of two independent samples, that

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is comparing the means of two independent
samples with unequal variances.

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If we are faced with this kind
of a question, we use a t-test.

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Again, if we are comparing the means
of two independent samples with

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equal variances, we still use a t-test.

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The underlying theory is that
when you're using a z-test,

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you're basing your results
on normal distribution, and

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when you are deploying t-test, you're
basing your results on t-distribution.

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And the process of
hypothesis testing could be

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made rather simple by
looking at these thresholds.

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If you are comparing the means and

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in the particular case you are looking
at the null being that the two

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averages are the same against
two averages not being the same.

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Then you're using a two-tailed test, and
in that particular case you're looking for

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a t-statistic or z-statistics of 1.96,
the absolute value of 1.96.

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If that were to be the case,
you reject the null hypothesis.

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That is,
you're conducting a two-tailed test.

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You can be using normal distribution or
a t-distribution, and

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you get the calculated z or t-statistics
of greater than absolute value of 1.96.

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And the expected p-value,

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the probability of that happening would be
less than 0.05 and you reject the null.

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The null being that
the two means are equal.

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In the case of one-tailed test,
where you're testing whether the mean or

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average of one entity is greater or
less than the other,

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here the absolute value for
z or t-statistic is 1.64, and

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the probability would
still be less than 0.05.

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If that were to be the case,
you reject the null.

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If the calculated value for z or
t-statistic is less than 1.96, you fail

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to reject the null hypothesis, and the
null being the two averages are the same.

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In case of a one-tailed test and
the calculated value for z or

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t-statistic is less than 1.64,
you fail to reject the the null and

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the null could be that one value or
the average is less than or

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equal to the other or
is greater than the other.