parameter estimation
Statistical inference mainly includes parameter estimation and hypothesis testing.
I. Sampling distribution
The population distribution is the distribution formed by all the observed values in the population.
There are usually population average, population variance and population proportion.
Reset sampling: there is Nn sampling mode, that is, samples with different Nn can be formed.
When the population obeys the normal distribution, the sample mean must obey the normal distribution. If the population is an unknown non-normal distribution, as long as the sample size n is large enough (usually n? 30), the sample mean will still be close to the normal distribution, the expected value of the distribution is the overall mean, and the variance is 1/n of population variance. This is the famous central limit theorem in statistics, which can be expressed as: take a random sample with a sample size of n from a population with mean and variance, and when n is large enough (usually n? 30), the distribution of sample mean approximately obeys the normal distribution with mean and variance of/n. If the population is not normal, the distribution of sample mean does not obey the normal distribution when n is a small sample (usually n < 30).
Overall proportion:? Sample ratio: p
The standard deviation of sample proportion can be expressed as: P= when the variance of population proportion? ( 1-? ) is unknown, and the sampling ratio P( 1-P) can be used instead.