This is Stephanie from StatisticsHowTo.com and in this video I'd be showing you on how
to support or reject a Null Hypothesis using a P-value.
We have a question here about a private high school principal who claims that his students
are above average intelligence. We've got a random sample of nine students
with their IQ scores. And we want to know is there sufficient evidence
to support principal's claim. The first thing we want to do is write our
hypothesis statement. If you don't know how to do this you can watch
my other video on how to state a Null hypothesis. For this particular statement we have the
Null, H sub-zero. The Mean population IQ is 100, so we've got that
the Mean is equal to 100. Our principal is claiming his students are
above average. So we want to change this equal sign to a
greater than symbol for our Alternate Hypothesis statement.
So we have two statements. Here I've drawn a picture, the piece we're really
interest is in this point here, and this is our critical value.
The way we figure out what this point is in the normal distribution is by using a formula.
Z equals Mean minus the population Mean, all over Standard Deviation divided by the square
root of the number of items in our sample. And if you substitute the numbers in this
question, we get Z is equal to 112.5 minus the population Mean of 100.
All over...the Standard Deviation is given as 15 in the question, divided by the square root
of 9. And if you work this out, it gives us a Z-value
of 2.5. We are going to look up 2.5 in the Z-table.
Here's my right hand Z-table and 2.50 is right here, 0.4938.
Right hand Z-table so it's telling me this area right here is 0.4938.
So I'm going to add 0.5, I'm going to add this area here.
This will give me the total area for this part of our normal distribution curve and
that would be 0.9938. Ok so we got this 0.9938 which is the area
on the left of this critical point right here. But what we are interested in, is the area on the
right of that point. And this is our P-value, this stands for Probability
value and this is the area we are interested in.
Well if we have this area and we want to know this area, we'll just subtract from 1.
So 1 minus 0.9938 gives us 0.0062. And all that is left to do is we compare our P-value,
0.0062 to the given alpha level 0.05. If the P-value is less than or equal to the
alpha level which it is, then we can reject the Null Hypothesis.
So our Null in this case is rejected. If the P-value had been greater than the alpha
level, then we could not reject the Null Hypothesis. Now what happens if you're not given this
alpha level? Let just say this is not here at all, and
then what do you do with this P-value of 0.0062? Well there are some general rules you can
use. Here there are, if the P-value is greater
than 0.1, you can't do anything. Where this really gets interesting is if your
P-value is below or equal to 0.05, then you can reject the Null Hypothesis.
If the P-value is very, very tiny which ours is 0.0062, it is much smaller than 0.1 then you
have highly significant results. So if you can feel confident in rejecting
the Null Hypothesis. However just bear in mind that these are just
guidelines. So if you are not given an alpha level, use
these guidelines. with a grain of salt unless
your P-value is very, very tiny. That's how to support or reject a Null Hypothesis
with a P-value. Check us out at StatisticsHowTo.com for more
videos and articles on everything elementary statistics.