00:01
A quaterer has determined that 87 % of the people who sample their food say it's delicious.
00:07
And they have a population, so do capital n for the population, of 5 ,000.
00:13
They took a sample of 144 people, and they were asked to sample it.
00:19
And we got p -hat.
00:21
P -hat is the proportion of the sample that say it's delicious.
00:26
What is the mean of the sampling distribution of p -hat? okay, so what is a sampling distribution? a sampling distribution is where you take every possible sample of 144, or generally size n, from the population.
00:42
So we get every possible sample, and we take the proportion of those samples that say they like the foods.
00:50
We know that the overall population proportion, p, is 87%.
00:56
The sample proportion is going to vary depending on what particular sample you take.
01:00
By just luck, you could take a lot of people who don't like the foods, and you'd have a very low p -hat.
01:07
Or a lot of people who do like it, you'd have a higher p -han.
01:10
So p -hat might be larger or smaller than 0 .87...