What is a Confidence Interval? Video Lecture | Mastering R Programming: For Data Science and Analytics - Database Management

[Music]
hi I'm Mike Maron today we'll discuss
the concept of a confidence interval for
a population mean when we do research we
often collect the sample and then we use
that data to calculate an estimate say
the mean of a variable but what if our
guess for the population mean relied
solely on the sample mean we got today
wouldn't relying on this single value be
problematic wouldn't other samples we
took tomorrow be different the sample
mean is our best guess at the population
mean but yes we know that this estimate
will differ a bit from the true value
due to what we call sampling variability
to account for differences that would
occur between samples taken today
yesterday or tomorrow we can attach a
margin of error to our estimate and be
reasonably confident that we will
capture the population mean this is the
idea behind a confidence intervals
suppose you wanted to take a sample to
estimate the mean length efficiently and
bear with me for a moment
but suppose somehow you could know the
true population mean length of fish in
this lake while our sample mean should
be reasonably close to that true mean of
40 centimeters we know that due to
sampling variability it won't be exactly
equal to 40 our estimate is just one of
many possible sample means we could have
ended up with on any particular day and
the sampling distribution describes this
theoretical set of all possible
estimates understanding the concept of
the sampling distribution of the mean
helps us attach a margin of error to our
estimate and create a confidence
interval man is getting late
rules of thumb are helpful things and
you should remember that we have one
rule of thumb that tells us that under
certain conditions about 95 percent of
all the sample means we could end up
with will be less than 2 standard errors
away from the true mean and if a sample
mean is usually less than 2 standard
errors away from the true mean then the
true mean is usually less than 2
standard errors away from the sample
mean in other words if we reach out
about 2 standard errors from a sample
mean we will usually capture the
population mean in this interval and
using the same rule of thumb we know
that about 5% of sample means will be
more than 2 standard errors away from
the true mean and in this instance
reaching out to standard errors from the
sample mean will not capture the true
mean of course we will never know how
far our estimate truly is from the true
mean we're only humble statisticians and
we must accept this we must accept our
limitations now let's get the heck out
of here and take a look at an example
suppose you are interested in estimating
the mean length of fish in this lake and
you only have this lousy lazy paper
cutout of a fisherman to help you let's
try something different to take a random
sample of 25 fish from this lake
for these 25 fish you find they have a
sample mean length of 41 centimeters and
a sample standard deviation of 12
centimeters now your best guess at the
true mean length of all the fish in this
lake is 41 centimeters but this my
friend is where we can bring in our
margin of error we can start from our
sample mean and reach out to standard
errors which is our margin of error here
on each side of the estimate to create a
95% confidence interval we would then
say that were 95% confident that the
true mean length of fish in this lake is
between thirty six point two to forty
five point eight centimeters and this my
friends is our confidence interval but
remember 5% of such intervals will not
contain the true mean we will never know
if our confidence interval actually
captures the true mean or not and we're
okay with that also remember the
standard error and hence the width of
the confidence interval will depend on
the sample size holding all else
constant as the sample size gets larger
the standard error will become smaller
and the confidence interval will become
narrower or more precise pretty
interesting stuff a in addition to
estimating the mean of a population
we're often interested in estimates that
summarize the relationship between two
or more variables such as differences in
means or correlations and things like
these we can construct confidence
intervals for these as well and they are
all based on the same concepts and
principles discussed here and all have
the same general interpretation in a
separate video we'll discuss how the
sampling distribution can be used to
test the hypothesis about a population
mean don't forget to check out the
statistics visualizations that accompany
this video you can find a link in the
description thanks for watching
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