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Sampling Distribution of sample means and central limit theorem - Coggle…
Sampling Distribution of sample means and central limit theorem
Tools of Business Statistic s
Descriptive statistics
-Collecting, presenting, and describing data either for population or sample information.
Inferential statistics
-Drawing conclusions and/or making decisions concerning a population based only on sample data
Populations and Samples
A Population is the set of all items or individuals of interest
Examples: All likely voters in the next election
All parts produced today
All sales receipts for November
A Sample is a subset of the population
Examples: 1000 voters selected at random for interview
A few parts selected for destructive testing
Random receipts selected for audit
Recap: Inferential Statistics
Making statements (inference or generalise) or drawing a conclusion about a population by examining sample results
Obtain a sample that is representative of the corresponding population is very important.
Sampling Theory and inferential statistics
Sampling distributions is to provide a logical basis for using samples to make inferences about populations.
ESTIMATING the unknown population quantities, such as population mean, variance, proportion.
Sampling theory is a study of the relationship that exists between a population and samples drawn from the population.
The population quantities that are estimated are called parameters, while the corresponding sample quantities are called sample statistic or statistics.
Sampling theory is also used in determining whether observed differences between two samples are actually due to chance variation or whether they are significant.
Example: In deciding whether new job training is better than old method involves HYPOTHESIS TESTING which are important in the theory of decisions.
Random Sample
A representative sample may be obtained by using a process called random sampling.
Random sampling is a process in which each member of a population has an equal chance of being included in the sample.
For a sampling theory and statistical inference to be valid, sample chosen must be representative of a population.
Sampling Distributions
Sampling Distribution of Sample Proportion
Sampling Distribution of Sample Variance
Sampling Distribution of Sample
Mean
Developing an understanding Sampling Distribution
Sampling Distribution Properties
If the Population distribution is NOT NORMAL
CASE 2: If the Population distribution is NOT NORMAL
We can apply the Central Limit Theorem:
If the random sample of n observations are drawn from a not normal population,
the sampling distribution of sample means will be approximately normal as long as the sample size is large enough.
Properties of the sampling distribution if n is large (n≥30) even if population is not normal:
The mean of the sampling distribution will equal the mean of the population : both and have the same value.
The standard error of the mean for the sampling distribution will equal the standard deviation of the population divided by the square root of the sample size.
3.The sampling distribution of sample mean will become approximately normally distributed when n is large (through CLT) or population distribution is normal.
Z-value for Sampling Distribution of the Mean
Z-value for the sampling distribution of :
