Khan Academy: Sampling Distributions

Question 1

How is the expected value and SD of sample distribution of sample proportion calculated?

Answer 1

E= P
SD=radical(P(1-P)/ n)
P=probability of success
n= sample size

Note: P(1-P) is the variance NOT standard deviation

A way of looking at it is that we have a bernoulli distribution and we are taking samples of the distribution, as with the normal distribution’s formula for sample distribution, the expected value of the sample distribution is equal to the population’s expected value, and its sd= population’s sd / radical(n)

Question 2

Under which conditions does the sampling distribution of sample proportion looks normal, skewed left, skewed right?

Answer 2

Conditions for normal distribution:
* nP>=10
* n(1-P)>=10
Condition for right skewed:
* When population proportion is so extreme relative to sample size that the number of expected successes<10 in sample
Condition for left skewed:
* When population proportion is so extreme relative to sample size that the number of expected failures<10 in sample

Example

Question 3

Is central limit theorem only true for means? if not, how does it work for IQR for example?

Answer 3

No, For IQR for example, the mean of the sampling distribution would equal the IQR of the population, and the sampling distribution of sample IQR would be normal