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Chapter 12 Sampling Distributions

Chapter 12 Sampling Distributions . James Van Slyke Azusa Pacific University . Sampling Distributions. Review Population Sample Inferential Statistics. Sampling Distribution of the Mean. Definition Taking several samples from a population Computing the mean of each sample

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Chapter 12 Sampling Distributions

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  1. Chapter 12 Sampling Distributions James Van Slyke Azusa Pacific University

  2. Sampling Distributions • Review • Population • Sample • Inferential Statistics

  3. Sampling Distribution of the Mean • Definition • Taking several samples from a population • Computing the mean of each sample • Forming a distribution of those sample means

  4. Sampling Distribution of the Mean • Characteristics of the sampling distribution • Resulting distribution is a distribution of sample means which itself has a mean and standard deviation • Mean of the sampling distribution of mean is signified by

  5. Sampling Distribution of the Mean • Characteristics of the sampling distribution • Standard deviation of the sampling distribution of mean is signified by • Standard error of the mean

  6. Sampling Distribution of the Mean • Central Limit Theorem • Describes the shape, mean, and variation • Shape • As sample size increases, sampling distribution of the means approaches a normal distribution

  7. Sampling Distribution of the Mean • Central Limit Theorem • Describes the shape, mean, and variation • Mean • Mean of sampling distribution equals mean of raw score population

  8. Sampling Distribution of the Mean • Central Limit Theorem • Standard deviation of the sampling distribution of mean is equal to the standard deviation of the raw score population divided by • Where n = the size of the sample • Thus, the standard distribution of means is narrower than the population distribution

  9. Normal Deviate (z test) • Used when the parameters of the Null Hypothesis are known (µ and σ) • Uses the mean of the sample as a basic statistic to test the null hypothesis • Must know the sampling distribution of the mean

  10. Computation of z • Calculate the sample mean • Use the following formula • Where

  11. Evaluating the Tail • Two-tailed probability – without valid basis for directional hypothesis, nondirectional used • One-tailed probability – Used for directional hypothesis • If there is a good theoretical basis • If there is other data supporting the conclusion

  12. Decision Rule • Alpha level – If the z score is • Less then or equal to the value of alpha or • More then or equal to the value of alpha • the null hypothesis is rejected

  13. Evaluation of z and H0 • Critical region for rejection of the null hypothesis • The area under the curve that contains all the values of the statistic that allow rejection of H0 • Critical value of a statistic • The value of the statistic that bounds the critical region

  14. Evaluation of z and H0 • Determine zcrit and assess whether zobt falls within the critical region for rejection of H0 • Critical Region of rejection is determined by the alpha level

  15. Homework • Chapter 12 p. 316 • 19, 22, 23, 25

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