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Chapter 10 – Sampling Distributions

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iola
8 diapositives · 292 Views · Oct 22, 2014

Sampling distributions are crucial for statistical analysis, providing insights into measures such as the sample mean and sample proportion. This chapter explores the sampling distribution of a sample statistic derived from repeated samples, focusing on the sample mean and its normal distribution properties. It discusses the Central Limit Theorem (CLT), highlighting how sample means tend toward normality with larger sample sizes, and introduces the z-score for determining probabilities related to sample means and proportions. Understanding these concepts is essential for drawing accurate statistical inferences.

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Chapter 10 – Sampling Distributions
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  1. Chapter 10 – Sampling Distributions Math 22 Introductory Statistics

  2. The Sampling Distribution of a Sample Statistic • The sampling distribution of a sample statistic is the distribution of values for a sample statistic obtained from repeated samples.

  3. The Sampling Distribution of the Sample Mean Let be the mean of a sample of size n from any population that has mean and standard deviation . For all sample sizes n, the sampling distribution of the sample mean: • Is exactly normally distributed.

  4. The Sampling Distribution of the Sample Mean • Is centered at , the mean of the population. • Has a standard deviation of , where is the standard deviation of the population. • Note: We don’t know what the true population mean and population standard deviation are.

  5. Central Limit Theorem (CLT) • The sampling distribution of sample means will become normal as the sample size increases.

  6. The Probability of the Sample Mean • Old z score • Note: This z score is used to calculate the probability of a single observation.

  7. The Probability of the Sample Mean • New z score • Note: This z score is used in calculating the probability of the sample mean.

  8. The Sampling Distribution of the Sample Proportion CLT Applied to the Sample Proportion. If the sample size n, is sufficiently large (both and are at least 5), then the sampling distribution of the sample proportion: • Is approximately normally distributed • Is centered at , the true proportion of success in the Bernoulli population. • Has a standard deviation of