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SAMPLING DISTRIBUTIONS

Explore the foundation of statistical inference with sampling distributions. Learn about parameters, statistics, variability, and sample proportions. Discover how the Central Limit Theorem shapes distributions of sample means.

jamesengel
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SAMPLING DISTRIBUTIONS

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  1. SAMPLING DISTRIBUTIONS . . . The foundation of statistical inference procedures Thanks to Ruth Reece, Jeanne Lorenson, and Susan Blackwell

  2. Before we talk about sampling distributions, make sure you understand the following: PARAMETER – a measure for an entire population, ex. STATISTIC – a measure for a sample, ex.

  3. What is a Sampling Distribution? A sampling distribution is the distribution of a set of values of a sample statistic obtained from all possible samples of a given size from a given population. Like any distribution, a sampling distribution can be described by its mean, standard deviation, and shape.

  4. A statistic is unbiased if . . . . . .the mean of the sampling distribution of the sample statistic equals the value of the population parameter being estimated. Examples:

  5. Variability of Sampling Distributions The larger the sample size of the samples, the less variable the sampling distribution will be.

  6. Format for Problems with Sampling Distributions • Get mean of sampling distribution based on having SRS. • Get standard deviation of sampling distribution based on population > 10n. • Establish if normal (will depend on what you are sampling). • Calculate probability.

  7. Sample Means

  8. Central Limit Theorem The CLT is about SHAPE. It says that the sampling distribution of sample means becomes more closely normal in shape as the sample size increases.

  9. What is Large? If n is 30 or larger, sample is large enough for distribution of means to be approximately normal. (Some books say 40, but 30 is ok) If n is larger than 15 with no outliers or apparent skewness, sample is large enough for distribution of means to be approximately normal.

  10. Suppose that the heights of Va. Tech students are normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. • What is the probability that a randomly selected student is taller than 5.5 ft tall? .344 2. What is the probability that the mean height of 30 students is greater than 5.5 ft? .014 3. Could you do #1 if the heights were not normally distributed? No 4. Could you do #2 if the heights were not normally distributed? Yes

  11. Sample Proportions

  12. Which of the following are true? • Sample parameters are used to make inferences about population statistics. • Statistics from smaller samples have more variability. • Parameters are fixed, while statistics vary depending on which sample is chosen. Answer: II and III (#I – no such thing as a sample parameter!)

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