M17 Hypothesis Test 2 SD Video Lecture | Mintab Tutorials for Beginners - Data & Analytics

so I have a new job I'm working in
purchasing for a health system now and
the Health System has been approached by
a manufacturer of a new IV pump and they
claim their IV pump while being far less
expensive is just as precise and
accurate as the IV pumps that the
hospital currently uses so the hospital
says Eric get one of the new IV pumps
and test it to compare it to the old IV
pumps and make sure that they have the
same precision so I'm really looking at
how much variation there is here I'm
really looking at standard deviations of
pump amounts so here's what I did I went
and I got an old pump one of our current
pumps whoops let me click here in this
window current pump and I test it by
running it at 60 milliliters per hour
for one hour and I do this 20 times and
you'll see I've recorded the results
here in column C one current for the new
pump I do the same thing do the same I
run it at 60 milliliters an hour for one
hour and I'm gonna do that 20 times and
I've recorded here exactly the amount of
fluid that came out each time so it
wasn't always exactly 60 but it's
usually pretty close to 60 I want to
know how precise is it how much
variation is actually exists in these
pumps and is there a difference between
them so I really want to compare they're
two standard deviations so first what
confidence level should we work at we're
gonna work at 95% confidence and we're
saying the claim that the company makes
is that the standard deviation of the
new pump is the same as that of the
current pump that we're using so we're
gonna test that
now does that claim a null or an
alternative hypothesis well that's an
equal statement that's a null we're
saying the SD of Nu is equal to the SD
of current and the alternative well if
I'm testing a quitclaim of equality the
best alternative is not equal is that
the SD of Nu is not equal to the SD of
current all right I got a slight problem
I don't actually have any problem
but the way that a test on two standard
deviations is done it isn't exactly done
where it's one equals the other and one
doesn't equal the other when we test two
standard deviations or two variances
what we do is we divide them we say one
divided by the other equals a certain
number so look back at this first one or
I'm gonna say this another way if the
standard deviation of the new pump
equals the standard deviation of the
current pump then if I took the standard
deviation of the new pump divided by the
standard deviation of the current pump
I'd really be saying it equals one so
let me phrase it a different ways
standard deviation of new divided by the
standard deviation of current equals one
that's the way it's going to work when
we do a test on two variances or two
standard deviations in Minitab or in
anything else so let me say the same
thing here here I'm saying the standard
deviation of the new divided by the
standard deviation of the current is not
equal to one so there I've got my
confidence level I've got my null I've
got my alternative I'm ready to run the
test where am I gonna go in Minitab well
I'm working with standard deviation
standard deviation is not an unbiased
estimator so I have to actually work
with variance I have two samples the
current pump and the new pump so I'm
going to say stat basic statistics and
I'm going to go to two variances
excellent each sample is in its own
column so I've got that but I want to
actually change these I want the sample
because of the way I wrote my standard
deviation or I wrote my hypothesis I put
new first and current second new on top
current on bottom
let me put new as sample one and current
as sample two all right let me click my
options my options this is exactly what
I want I want standard deviation divided
by standard deviation I could make it
variance divided by variance but we're
working in standard deviations here my
confidence level 95 my hypothesized
ratio is one right there of that one and
I'm working with a not equal as my
alternative so this is great I'm gonna
say okay and I'm gonna say okay now
Minitab is going to make a pretty graph
for me where they put a bunch of things
together and really I could just look at
this graph because all I care about is
these p-values bonnets test or the
means test our book talks about the
f-test Minitab is doing it by a better
version but it doesn't matter because
I'm going to get the same conclusion
regardless but if you don't want to look
at the graphs
it's given me a graph of this is what
the confidence intervals of the two of
them actually look like and so on or I'm
sorry here's the confidence intervals
for the standard deviations of the two
they do look kind of different but I'm
looking at those p-values if I went over
here it also gives me the p-values in
the main session window as well so
either way the p-value is high I'm
working at 95% confidence or
significance of point zero five this
p-value is 0.16 2 or 0.15 4 depending on
which test you look at either way the P
is high the P is high the null can fly
hey no you get to stick around so what
do we say we say there is not sufficient
evidence to contradict the claim that
the standard deviation of the new pump
is the same as the current pump so good
news for the guy who's making the new
pump I guess maybe we're going to be
buying them if they're really less
expensive