00:01
For this problem, we're told that an experiment on the side effects of pain relievers assigned arthritis patients to take one of several over -the -counter pain medications.
00:08
Of the 453 patients who took one brand of pain reliever, 25 suffered some adverse symptom.
00:16
We're asked, does the experiment provide strong evidence that fewer than 12 % of patients who take this medication have adverse symptoms? so, first step here is going to be to find our test statistic.
00:30
Particularly.
00:32
So, pardon me, the test statistic here is going to be the z score, or z score is going to be given by the observed proportion, so 253, which is about 0 .055, is how we'll round that, 0 .055, minus the null hypothesized proportion, 0 .12, divided by the square root of the null hypothesized proportion 0 .12 times 1 minus 0 .12 over n, which in this case is 453.
01:11
So let's calculate out our z score here, 0 .055 minus 0 .12 over root 0 .12 times 1 minus 0 .12, divided by 453.
01:24
Gives us a z score here of approximately negative 4 .23, which we can bring up a standard normal distribution here and test this for our z score our hypothesis okay our yeah we're doing a left -tailed hypothesis test so we go left tail put this at negative 4 .23 and rounded to four decimal places the p value is about 0 .0 000 zero zero it's roughly zero then for the second problem shown each of 42 subjects tastes two unmarked cups of coffee and says which he or she prefers one cup in each pair contains instant coffee the other fresh brood coffee we have that 25 of the subjects prefer the fresh brood coffee we're told to take p to be the proportion of the population who would prefer fresh brood coffee in a blind tasting we test the claim that a majority of people prefer the taste of fresh -brood coffee.
02:33
So again, we'll just be calculating out a z score here.
02:38
Our observed proportion is 25 over 42...