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Sampling distributions

Sampling distributions. Warm-up. My friend has a dog named Jake. He is an adult dog and weighs 25 pounds. Decide if Jake is a golden retriever. How certain are you that your answer is correct?. Warm-up. Jake is a Welsh Corgi!.

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Sampling distributions

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  1. Sampling distributions

  2. Warm-up • My friend has a dog named Jake. He is an adult dog and weighs 25 pounds. • Decide if Jake is a golden retriever. • How certain are you that your answer is correct?

  3. Warm-up Jake is a Welsh Corgi! • What if I had asked you to make a judgment about a breed of dog with which you were not familiar?

  4. Sampling Distributions Objective Purpose • To answer the question, “What are sampling distributions, how do we simulate them, and what is their importance in the study of statistics?” • So you can answer specific questions with a known degree of confidence (statistical inference).

  5. Parameters vs. Statistics Random selection Sample Population or or (Statistic) (Parameter)

  6. Sampling Variability • The value of a statistic varies in repeated random sampling. This is known as sampling variability. • What would happen if we took many samples?

  7. Sampling Distribution • The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population. • Example: Let the population be the integers 0-9. Frequency Value of sample mean in sample of size n=2

  8. Let’s Simulate a Sampling Distribution!

  9. Bias and Variability Bias Variability • A statistic used to estimate a parameter is unbiased if the mean of its sampling distribution is equal to the true value of the parameter being estimated. • The variability of a statistic is described by the spread of its sampling distribution. • Larger samples give smaller spread.

  10. Bias and Variability • Properly chosen statistics computed from random samples of sufficient size will have low bias & low variability.

  11. Let’s Create another Sampling Distribution! Young Women’s Heights

  12. Exit Ticket • Your individual answers to the “Young Women’s Heights” questions. • “What are sampling distributions, how do we simulate them, and what is their importance in the study of statistics?” • Have a great day! 

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