Confidence Intervals; Appropriate Sample Size - StatCrunch Video Lecture | Statcrunch Tutorials for Beginners - Data & Analytics

hey class this is mr. Woodbury just a
short video to go through the main ideas
from the problems in chapter 9 I'm going
to be doing a few problems from the
chapter 9 project using statcrunch so
that we can get used to the steps first
problem is a confidence interval for a
proportion and basically here being
asked to construct a confidence interval
or give an estimate of a proportion of
all cos students who owned an iphone for
a proportion also remember the data are
categorical so here we died so soon do
you have an iPhone their answer would be
yes or no and look for this idea of 30
out of 125 this many out of that many
all right let's go over to star crunch
and the steps we want to take for a
confidence interval for a proportion
stat proportion one sample with data
with summary the number of successes was
30 the number of observations was 125 30
over 125 is P hat the sample proportion
let's see here we want confidence
interval it did say 95 percent so we'll
leave the level alone and never change
the method always leave that the same
when we click on compute we get our
confidence interval here in the lower
right hand corner point 1 6 5 1 is the
lower limit point 3 149 is the upper
limit and we say we're 95% confident
that the proportion of all cos students
that own an iPhone is between point 1 6
5 1 and point 3 1 4 9 let's move on to
the second problem confidence interval
for a mean here again we're being asked
to construct a confidence interval it
says for the mean also if you think
about the data here these would be
Numerical because we would be writing
down the mileage for each car the sample
information we need sample size and is
15 sample mean x-bar is seventeen point
nine and sample standard deviation s is
three point nine we do need to make note
of the level of confidence here it was
95 percent so we can go ahead and do
this in statcrunch hope I can remember
all those numbers this is under stat T
statistics one sample this time we have
summary because I have the mean and
standard deviation but if we had the
actual data we would choose with data
instead so with summary we want to write
down the sample mean I believe that was
let's make sure seventeen point nine for
the mean a standard deviation was three
point nine and the sample size was C
fifteen cars so we'll type in 15 for the
sample size we wanted a confidence
interval so we click that radio button
it was 95 percent so we'll leave that
alone
click compute and we're 95% confident
that the mean mileage is between fifteen
point seven four and twenty point zero
six rounded to two places when you do
these problems in my math lab or my stat
lab just pay attention to where they
asked you to round them the other two
types of problems
in chapter nine involve finding the
appropriate sample size the first one
I'm going to show you is for a
proportion a student wants to estimate
the percentage of college students who
smoked and we're asked for how large of
a sample right that is the clue that
here we're looking for a sample size and
not to estimate also we don't have a
sample to work with ninety percent is
the level of confidence and we want to
be off by no more than four point five
percent that means that the margin
error is 0.04 5 now in statcrunch we
need to know the width of the interval
and that's 2 times the margin of error
which is point zero nine okay so in
statcrunch we can work this one through
by clicking on the stat proportion one
sample this time we want the option
power slash sample size and we're going
to be working with the sample size click
on the right tab for confidence interval
width
confidence level gets entered first
that's 0.9 or point 90 the target
proportion if you had an estimate of
what the proportion was you would enter
that here we have no idea so I'm going
to leave that is 0.5 what that does is
it give us gives us the largest possible
sample the mistake we make is simply too
many which is a better mistake than
sampling too few okay for the width we
want to type in our margin of error
times two that was point O 9 leave
sample size blank and when we click
compute we get our sample size for the
problem of 335 let's head back to the
problem I know this was a proportion for
a couple of reasons one talks about the
sample proportion second we're looking
for a percentage of students who smoke
the data would be categorical do you
smoke yes or no and finally the margin
of errors given as a percentage that's
another good clue all right let's go to
the last problem I'll show you this is
when we're trying to estimate a mean and
we look for the sample size okay how
large of a sample is required tells me
we're looking for the sample size not
the estimate we want the mean to be off
by no more than two hours
that's the margin of error we also need
an estimate of the standard deviation
and an initial study showed that that
was approximately eight point three
hours finally again you do need
you know the level of confidence this
time we want to be pretty confident 99%
back to statcrunch this one is under
stat Z statistics so we don't use T
we're gonna use Z for this one one
sample again sample size click on the
right tab for confidence interval width
our confidence level this time was 0.99
we know that the standard deviation was
given in the problem as 8.3 so I'm going
to enter that 8.3 and the width of the
interval this time the margin of error
was 2 so the width would be 2 times that
margin of error or 4 so let's go ahead
and enter that again leave the sample
size blank and click compute and we get
a sample size of 115 all right so I hope
that helps you construct a confidence
interval when you're asked to construct
a confidence interval or to make an
estimate compute the sample size when
you're not asked for the estimate but
instead how large you a sample will you
need to ensure these particular results
you also need to know the difference
between proportion and mean proportion
you want to think about is the data
categorical also look for clues for a
confidence interval the sample will be
this many out of that many for a sample
size problem the margin of error is
usually given as a percentage when we're
talking about means the data will be
numerical or quantitative and pretty
much the key number there's-- standard
deviation if you see standard deviation
you're pretty much dealing with the mean
however you should be able to read
through the problem
and understand what it's asking for not
just look for key values all right good
luck with this everybody