Hypothesis Test for a Proportion Using StatCrunch Video Lecture | Statcrunch Tutorials for Beginners - Data & Analytics

in a previous poll 33% of adults with
children under the age of 18 reported
that their family ate dinner together
seven nights a week
suppose that in on more recent poll 332
1050 adults with children under the age
of 18 reported that their family ate
dinner together seven nights a week is
there sufficient evidence that the
proportion of families with children
under the age of 18 who eat dinner
together seven nights a week has
decreased at the Alfa's point one level
of significance so what we want to do
first is establish a null and
alternative hypothesis so the null
hypothesis is a statement of no change
no different status quo would be what P
equals 0.33 that's the results from the
previous poll we're looking to gather
evidence to suggest that P has done what
decrease so our alternative would be
that P is less than 0.33 and now what we
want to do is verify that we can use the
normal model in order to approximate the
p-value and so to use the normal model
what do I need to be true n times P
times
that's one - she needs to be at least
ten so as a thousand fifty we haven't
figured out P yet have we oh yeah we
have P is 0.33
and what we get for that 232
up to 32 which is certainly at least 10
so the normality requirement to satisfy
and now I need my independence
requirement to be satisfied so I need to
sample size to be no more than 5% of the
population size we surveyed a thousand
50 adults with children under the age of
18 I'm certain that there's at least 10
million of those types floating around
the country yes and 5% of 10 million is
500,000 and so 500,000 is certainly
bigger than 1,050 so we're good to go on
the independence requirement as well and
so now we have that our level of
significance alpha is what 0.1 and so
the third step is to come up with a
p-value we're going to go ahead and use
statcrunch to get our p-value yes so we
go over to statcrunch and we go to stat
proportions one sample we have summary
data how many successes do we have
332 are still eating together seven days
a week so that's a success 332 - and we
surveyed a thousand 50 individuals yes
we're doing a hypothesis test what's the
statement in the null point three three
and the direction in the alternative is
less then click calculate and there are
results
so here we're getting a p-value of 0.1
7:06 see it p-value point one seven zero
six and here is our sample proportion it
was 0.316 so the question we're really
asking ourselves is how likely is it to
get a sample proportion of 0.14 0.316 or
less if the population proportion is
0.33 put another way how likely is it to
get 332 or fewer families that eat
together out of a thousand 50 if the
true population proportion is 0.33 so
our p-value point one seven would be
interpreted as follows if we obtained
100 samples of size a thousand and fifty
from this population
we would expect about how many seventeen
to result in 332 or fewer families
but eat together if the population
proportion is what 0.33 so the real
question is are the results that we got
unusual under the assumption of
population proportion is 0.33 is the
evidence statistically significant that
the proportion of families that eat
together is gone down well is 17 out of
100 and amuse result if you observe
something happens 17 times out of 100
are you saying whoo that's weird no
probably not and so would you be willing
to say the proportion of families that
eat dinner together has gone down based
on the results that you see no you would
not because you observe something which
is going to happen about 17 times out of
100 if the population portion still is
0.33
so this tells us do not reject H naught
the p-value is not less than a lot of
significance the p-value is greater than
the level of significance remember if
the P is low the null must go this
p-value is not low so our conclusion
here is there is not sufficient evidence
to suggest the proportion of families
with children under the age of 18 as
decrease from 0.33
bear in mind we're not saying that the
proportion is 0.33 we're simply saying I
don't have enough evidence to say it's
not 0.33 big difference