00:02
Hey there, welcome to numerate.
00:05
So we have 5 % of the nation's children is said to be born with congenital abnormalities in the 1980s.
00:14
We want to see if this number of abnormalities has increased over time.
00:19
So our claim is that the congenital abnormalities has increased using a 0 .05 significance level.
00:30
Okay, so with that, we're going to start with 22.
00:42
With our noaa and alternative hypothesis.
00:49
Let's start with our alternative, which is our claim, that the risk of congenital abnormalities has increased.
00:58
We'll do with proportion here.
01:01
So if it has increased, it should be greater than that initial 0 .05 in 1980, right? and then our noaa hypothesis would equal that 0 .05, because that's what the first sentence of our prompt says.
01:16
Okay.
01:16
Now let's go to, so that would best match with answer a.
01:22
Let's go to 23.
01:25
What would the standard error be for this problem? so the standard error is basically the proportion.
01:43
So basically is the proportion divided by.
01:55
So if we look at the test, the test stat, and the standard error it will be quite similar okay so it will basically equal to the square root let me see that so let me fix that the standard error equals the square root of basically the p hat minus or times one minus p hat and that entire equation right there will be divided by n okay so again our p hat is our proportion sample proportion right so let's try calculator sample proportion okay it will be let's put it up here we can put up here p hat equals 23 divided by 33 3834 384 that equal proportion of around 0 .0 5 0 .060 so let's put plug the end 0 .060 1 minus that so it's going to be 0 .94 divided by n right sample size over here is 384 okay, so let's punch that into our calculator and see what we will get.
04:55
So our sample size is 0 .04, so the square root, basically 0 .06 times 0 .94 divided by 384.
05:27
Okay, so i got around 0 .033.
05:37
Let's actually carry our decimals in to be exact, okay? let's see.
06:06
449.
06:14
Let's carry the decimals this time, so it's gonna be 0 .059, 599 times 1 minus 0 .0599 divided by our sample size, 384.
06:54
0 .0 so it would be around 0 .013 okay so it will be b times that so it will equal around 0 .013.
07:42
Okay, let's move on to 24.
07:45
I test that so our z score so we have our proportions subtracted by each other so we have 0 .060...