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Chapter 9 Notecards

Chapter 9 Notecards. 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

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Chapter 9 Notecards

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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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