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Understanding Sampling Distributions in Statistics

Learn about parameters, statistics, and sampling distributions in statistics, with details on variability, unbiased samples, and the Central Limit Theorem. Explore sample proportions and sample means and their distributions.

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Understanding Sampling Distributions in Statistics

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  1. Chapter 9Notecards

  2. Sampling Distributions Parameter – number that describes the population Statistic – number computed from the sample data (used to estimate the parameter) Sampling Distribution – the distribution of all values of the statistic for given n Variability – estimate will vary from sample to sample (described by the spread of sampling distribution) larger samples give smaller spread Unbiased Sample – the mean of the sampling distribution is equal to the true value of the parameter being estimated Note: as long as the population is 10 times larger than the sample, the spread is approximately same for any population size.

  3. Central Limit Theorem When n is sufficiently large, the sampling distribution of x is well approximated by a normal curve, even when the population distribution is not itself normal.

  4. Sample Proportions Choose an SRS of size n from a large population with proportion p (Let be proportion of sample) • Sampling distribution of is approximately normal if np ≥ 10 and n(1-p) ≥ 10(Becomes more normal as n increases) • Mean of sampling distribution of is exactly = p • S.D. of sampling distribution = if pop is at least 10 times sample • As n increases, approaches p and variability and S.D. decrease.

  5. Sample Means Choose an SRS of size n from a large population with mean µ and S.D. σ (Let be mean of sample) • Sampling distribution of is approximately normal if n ≥30(Becomes more normal as n increases) • Mean of sampling distribution of is exactly = µ • S.D. of sampling distribution S.D.= if pop is at least 10 times sample • As n increases, approaches µ and variability and S.D. decrease.

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