00:01
We are told that 75 % of people support a particular issue.
00:04
We take a sample of size 800.
00:07
So the probability each person supports this issue should be 75%.
00:11
What is the probability that the proportion who support the issue in this sample is between 74 % and 76 %? so we want the probability the sample proportion p -hat is between 74 % and 76%.
00:28
Notice i've switched to decimal form here.
00:31
That's because we're going to do some calculations and percentages don't play well with calculations.
00:37
So it would be great if i knew the distribution of sample proportions.
00:42
Looking at this initially i see a binomial distribution.
00:45
We have n independent trials, two outcomes, they support it or they don't, same probability p for each of them.
00:52
The binomial variable is x, the number from a sample of this size that meet the criteria.
00:58
I'm going to take a normal approximation to this binomial.
01:01
So now we're going to have a normal curve, or approximately normal.
01:09
Its mean is np, its standard deviation root np1 minus p.
01:16
These are just the mean and standard deviation of a binomial, but they're the mean and standard deviation of x.
01:23
I don't want a probability for x, i want a probability for p -hat.
01:27
So to go from the number who support the issue in the sample to the proportion in the sample who support the issue, i'm going to divide this distribution by n to get my sampling distribution...