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Section 8.1 Distribution of the Sample Mean - Coggle Diagram
Section 8.1 Distribution of the Sample Mean
sampling error is the error that results from using a sample to estimate information regarding a population
unless we sample every single individual in the population there will be some error in our results
Vocab
sampling distribution is a probability distribution of a statistic obtained through a large number of samples drawn from a specific population
shows every possible result a statistic can take in every possible sample from a population and how often each result happens
The Law of Large Numbers: as n increases, the difference between X and u approaches zero
x = sample mean u= population mean
Central Limit Theorem regardless of the distribution shape of the population the sampling distribution of x becomes approximately normal as the sample size n increases
the distribution of the sample mean will always become normal as the sample size increases
you want your sample size to be about 30
Distribution of the sample mean IS it normal
Shape: Approximately normal if n > 30 or the population is normal
it has to be at lest 30 in order to be used
Center: Mean:
Spread:Standard deviation
is the standard error of the mean
As n (sample size) increasres the standard deviation decrease
Standard error means the standard deviation of the distrubution of sample
Independence
For any characteristics of the distribution of the sample mean to hold we must be able to assume independence between observations
-Random sample
Correct Notation
Mean (Center)
Mean of a sample is
Population
Sampling distribution of the mean
Mean of all the sampled means
Standard Deviation (Spread)
sample
Population
Sampling Distribution of the Mean
standard error of the mean
