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In this video, I will
illustrate how to state

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your hypothesis when you're

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comparing the averages
between two entity.

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We will use basketball
as an example,

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using Michael Jordan
and Wilt Chamberlain,

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the two highest scorers in

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the history of
basketball, as examples.

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If you were to recall,

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you would know that Michael
Jordan, on average,

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scored 30.12 point in each game,

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and Chamberlain averages
around 30.06 points per game.

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If you were to compare

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the two averages between
Michael Jordan and Chamberlain,

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and even though they are very
similar looking numbers,

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we need to set up a statistical
hypothesis testing.

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We are interested in comparing

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the average points scored by
the two basketball players,

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and the comparison of means or

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averages is available
in three flavors.

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First, we can assume that

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the average points per game
scored by the two players,

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Jordan and Chamberlain,
are the same.

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That is, the difference between

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their mean scores is zero.

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If their averages are the same,

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average of one minus average
of other should be zero,

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this becomes a null hypothesis.

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Let's say if Mu_j

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represents the average points

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per game scored by
Michael Jordan,

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and Mu_c represents
the average points

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per game scored by
Wilt Chamberlain,

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we can state the null hypothesis
to be Mu_j equal Mu_c,

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that is the average scored by

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Jordan and average scored by
Chamberlain are the same.

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The alternative hypothesis
would be that no,

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these averages are not the
same, they are different.

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The alternative hypothesis H_a

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compared to null
hypothesis H_0 or o.

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The alternative is that the
averages are not the same,

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their average scores
are different.

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Now, the other option,
the second option,

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is to assume that Jordan
scored better or higher.

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In that case, our
null hypothesis is

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the average score by

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Michael Jordan is greater than or

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equal to the average score
by Wilt Chamberlain.

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In this particular case,

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the alternative hypothesis
would be different.

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It wouldn't be not equal to,

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but it would be less than.

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The alternative would be
that the average scored by

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Jordan is less than that
by Wilt Chamberlain.

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By the same account,

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our third option will be

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that the null hypothesis is
that in fact Jordan scored

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less than Wilt Chamberlain and

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the alternative hypothesis
will be the reverse of it,

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saying that no,
Michael Jordan scored

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higher than Wilt Chamberlain.

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In a nutshell, we
have three options.

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We can say the averages are the

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same and the null would be,

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no, they are not the
same, not equal.

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We can say the
average is less than,

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the null is that Jordan's average

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is higher than Chamberlain,

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and the alternative would
be the reverse of it.

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The third option is to say that

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the average scored by

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Jordan is less than average
scored by Chamberlain,

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and the reverse of it will be
the alternative hypothesis.

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So, three ways of
defining a hypothesis.