Sampling Distributions Key to Statistical Inference

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Presentation transcript:

Sampling Distributions Key to Statistical Inference Jim Bohan Manheim Township School District Lancaster Pennsylvania jim_bohan@mtwp.k12.pa.us

The Sampling Process SAMPLE POPULATION 

The Sampling Distribution The Sampling Distribution Repeated Sampling POPULATION  Sampling Distribution

And the Sampling Distribution is? If the sampling fits the criteria for the Central Limit Theorem, we can recognize the Sampling Distribution. For example, SRS and Normal Population or Large Sample

Elementary Sampling Distribuitions Normal (, ) t-distribution (df) Chi-square (df)

If the Sampling Distribution is known… Probability questions about sample statistics can be answered. For example, A simple random sample of 50 is selected from a normal population with a mean of 50 and a standard deviation of 10. What is the probability that the sample mean will be greater than 53?

The Answer… A simple random sample of 50 is selected from a normal population with a mean of 50 and a standard deviation of 10. What is the probability that the sample mean will be greater than 53?

Two Deceptively Similar Problems Census data states that the mean height of adult males in a city are normally distributed with a mean of 69.2 inches and a standard deviation of 4.3 inches. A sample of 35 is selected. What is the probability that one of these subjects has a height greater than 70 inches?  DATA DISTRIBUTION Census data states that the mean height of adult males in a city are normally distributed with a mean of 69.2 inches and a standard deviation of 4.3 inches. A sample of 35 is selected. What is the probability that the mean of these subjects has a height greater than 70 inches?  SAMPLING DISTRIBUTION

The Key to Significance Testing

Another Example