In this video we'll take a look at null and alternative hypotheses and
specifically we'll take a look at some examples using a one tailed test. So
let's say we're looking at the problem here where we're trying to evaluate
whether a new tutoring method results in higher scores on a math exam. It assumed
here that the average math score using the existing method is mu or a mean of
80 now if we're doing a one-tailed test here notice that I've underlined higher
so we're looking for scores that are higher than or greater than 80 and as I
had said in a previous video when we're doing one tailed tests I really think
it's a lot easier to start with the alternative hypothesis. So let's take a
look at that and for the alternative we want to see higher than 80 so you can
see here our alternative states mu is greater than 80 and recall that the null
is everything but that so the null is notice we have the same mu the same
value of 80 but instead of greater than it's less than or equal to 80. Let's go
ahead and take a look at another example. Does a new customer service approach
result in greater satisfaction among clients and notice the one tailed or
directional statement here greater satisfaction so what we'll do here in
this example is we have a new customer service approach and we'll just consider
the existing approach as the old approach for this example so is mu
greater than the old so the alternative shows that the mean for the mu is
greater than the mean for the old and the mean here is satisfaction customer
satisfaction now the null hypothesis once again is everything but the
alternative so notice we have the same symbols here once again the mu new, mu new, mu old, mu old, but instead of greater than, now we have less than or equal to
once again. Okay as another example - Are conversion rates higher
with a new landing page? So here we'll do new page vs. old page again. So the
alternative and this is a proportion here so the proportion of conversions
like .06 or what have you. The proportions under the alternative
for new is greater than old and that's because we see our conversion rates
higher with the new landing page so alternative new is greater than old and
in the null would be everything but that so mu is less than or equal to old
and then as our last example here here we'll do one that's the opposite
direction so, does a new medicine result in lower cholesterol levels than an
existing medicine? So we'll call the existing old once again so is new lower
cholesterol than old? So our alternative should state that here we have mu that's
the mean cholesterol level for new is less than the mean cholesterol level for
old so mu is less than old and the alternative is everything but that for
one tailed test so the new is greater than or equal to old for one tailed
tests notice how the alternative hypotheses are always either statements
of greater than or less than so reviewing the four we looked at we had
mu is greater than 80 the new is greater than the old the new once again
is greater than the old but this time looking proportions and then finally our
last example we have the new was less than the old now the key here is every
alternative are H1s are always either greater than or less than and for each
test the null hypothesis is always the opposite sign of the alternative and the
= to sign so in our first example where we have the alternative the mean
was greater than 80 the null is everything else everything but that so
if the mean is greater than 80 for the alternative the null is the mean is less
than equal to 80 and then for a second example if the alternative was the MU of
MU is greater than old then the null is everything else so less
than or equal to and then we see that again with our third example greater
than for the alternative less than or equal to for the old and then finally
for our last example here the alternative was new is less than old so
the null was everything else greater than or equal to and notice here again
that everything is duplicated so we have new old new old the same thing here it's
always duplicated all the changes between the null and the alternative is
the sign so if this is greater than we already know that the null is everything
else less than or equal to if this is less than we already know that the null
is everything else greater than or equal to. Okay that's it for examples with one
tailed tests in hypothesis testing. Thanks for watching!