00:01
We have a previous study indicating that 68 % of americans support the death penalty.
00:06
We want to know if that is still the case today.
00:10
So our null hypothesis, h0, the null hypothesis is always that things have not changed or there is not a difference.
00:18
So our null hypothesis is that the population proportion p is still 68%.
00:23
Our alternative hypothesis is that this has changed.
00:30
We want to know if it still holds today, so we want to know has it changed or not.
00:35
So that would be that p is not 68%.
00:38
To test this we take a sample of size 500 and we're going to find the sample proportion.
00:48
We found in this particular case that 320 of them support the death penalty.
00:54
Okay so we want to know p, the population proportion, to compare it to 68%.
01:00
But we can't ask every single american, so we take a sample and we want to know if that sample proportion is close enough to 68 % that we don't reject the null hypothesis.
01:14
So the probability of our proportion being exactly 68 % is very low, even if the population proportion is 68%.
01:21
So we need an idea of what normal outcomes would look like here, and that is given by an approximately normal curve.
01:31
This is the sampling distribution.
01:34
It is a probability curve showing you the different sample proportions you might get for a binomial experiment with 500 independent trials, probability 0 .68 of success.
01:49
Totally arbitrary term here.
01:53
So the mean of the sample proportions is just p, so that's 0 .68.
02:01
The standard deviation of the sample proportions also called the standard error is root p1 minus p over n.
02:10
And both of these you just get them by taking the mean and standard deviation of a binomial distribution and dividing them both by n...