Question

What is a sampling distribution?
What is a point estimator of a parameter?

Answer 1

What is a sampling distribution?

the distribution of a statistic(numerical summary of the sample) is called a sampling distribution.

for large samples n>30,sample follows normal distribution ,

Central Limit Theorem CLT
Sampling Distribution of the Sample Mean
For a random and representative sample (SRS) with a large sample size n, the

sampling distribution of the sample mean is

approximately normal with mean μ (same as the original distribution) and
standard error = (the original standard deviation divided by the square root of n).

Sampling Distribution of pˆ
is approximately normal, with mean = p and standard error =sqrt(p*(1-p)/n

as long as the expected number of successes (np) and failures (n(1-p)) are each 15 or larger.

What is a point estimator of a parameter?

A point estimator is a statistic for estimating the population parameter

A good point estimator should be unbiased,the expected value of the estimator must be equal to the mean of the parameter

sample mean,xbar is unbiased etimator of population mean,mu

sample standard deviation is an unbiased estimator of popualtion standard deviation ,sigma

sample variance is an unbiased estimator of popualtion variance ,sigma^2