What is a Hypothesis Test and a P-Value? Video Lecture | Mastering R Programming: For Data Science and Analytics - Database Management

hi I'm Mike Mary today we'll discuss the
concept of a hypothesis test for a
population mean we call this a one
sample feature
now we often collect data and then we
use that data to calculate an estimate
say the mean of a variable we may
hypothesize that the true population
mean is greater than less than or
different from some value we can use a
hypothesis test to test the claim about
the true mean take this lake as an
example sustainable fishing regulations
dictate that we must let fish mature and
fishermen may only begin fishing once
there is convincing evidence that the
mean length of fish in the lake is
greater than 35 centimeters of course we
cannot measure all the fish in this lake
and so instead we take a random sample
let's take a look at a sample of 25 fish
we can see that for these 25 fish the
sample mean length is 41 centimeters and
the sample standard deviation of the
lengths is 12 centimeters now our
estimate of the mean length from our
sample is greater than that 35
centimeters we require in order to begin
fishing in the lake but we know that
sample means vary around the true mean
and are not exactly equal to the true
mean we also know that we're hungry
really hungry and we want to get back to
fishing as soon as we can it's on us to
provide convincing evidence that the
mean length of these fish is greater
than the 35 centimeters so we can start
fishing let's get started we'll begin
with a question do we believe that the
mean length of fish in this lake is
truly greater than 35 centimeters
or do we think our sample estimate of 41
ended up being greater than 35
centimeters merely by chance in other
words is there enough evidence to claim
the true mean length really is greater
than 35 centimeter man oh man do I hope
so to answer this question we will begin
by assuming that the mean length of fish
in the lake is 35 centimeters the
authorities won't let us fish unless the
average length of fish is larger than 35
centimeters from here we can calculate
something called a p-value which
measures how compatible our 41
centimeters sample estimates is with
this assumed value of 35 centimeters we
would like to use our sample of 25 fish
to try and make a statement about the
population at large let's start with a
hypothesis or in other words an
assumption let's assume that the true
mean length of fish in this lake is 35
centimeters this is what we call a null
hypothesis we begin by assuming this to
be true that the true mean length of
fish in this lake is 35 centimeters
since we don't know the true standard
deviation we will substitute in the
sample standard deviation in order to
estimate the standard error of the mean
recall that the standard error of the
mean gives us an idea of typically how
far a sample mean will deviate from the
true mean we would then know what the
sampling distribution of the mean would
look like under this null assumption
that the true mean is 35 centimeters
recall we've taken a sample of 25 fish
from the lake and found them to have a
sample mean length of 41 centimeters we
can then ask the following question
under our null hypothesis that the true
population mean length of fish is 35
centimeters what is the chance that we
end up with a sample mean length of 41
centimeters or more this probability is
the p-value if we were to calculate this
probability we would find that it's
approximately one percent or one in a
hundred in other words if the true mean
length really is 35 centimeters and we
took 100 different samples of 25 strips
we'd expect that only one of the 100
samples would give us an average length
of 41 centimeters or more just by chance
from here we can conclude that one of
two things must have happened either our
initial assumption that the mean length
is 35 centimeters is correct
and we ended up with a fairly rare
estimate of the sample mean 41
just by chance or our initial assumption
is incorrect and the true population
mean really is greater than 35
centimeters we of course will never know
for sure which of these is true in
reality but we can decide which we
believe is more likely to be true so how
small should our p-value be before we
will reject our null assumption a
general rule of thumb is to reject our
null hypothesis if the p-value is less
than 5% and what's so special about that
5% cutoff you ask it's because Sir
Ronald Fisher suggested this as a
reasonable cut point and it's stuck it
is a reasonable yet arbitrary choice
based on our p-value of 1% we will
reject our null hypothesis and conclude
that we have enough evidence to claim
that the true mean length is greater
than 35 cents
be careful relying solely on the p-value
can be a dangerous thing as it does not
allow us to make any statements about
the precision of our estimate to
strengthen our analysis we should also
construct a confidence interval for the
mean previously we learned how to do
this we would say that we are
approximately 95% confident that the
true mean length of fish in this lake is
between 36 point two to forty five point
eight centimeters the entire range of
acceptable values are all above the null
value of 35 centimeters which is in line
with our conclusion that the true mean
is greater than 35 centimeters can I get
some tartar sauce over here please
in addition to testing hypotheses about
the mean we're often interested in
testing hypotheses on estimates that
summarize the relationship between two
or more variables we can test hypotheses
for these as well and they're all based
on the same concept here don't forget to
check out the statistic visualizations
that accompany these videos you can find
the link in the description thanks for
watching
I know I know together will