## Lesson 8: Sampling Distributions and the Central Limit Theorem

September 25, 2019

Review:

- Exam 1 Results
- Design of Experiments
- Census and Sampling
- Sampling and Surveys

Presentation:

- Sampling Distributions
- Take multiple Simple Random Samples, sample size = n, and calculate each sample mean
- “Sampling Distribution” is the distribution of sample means
- Standard deviation of sample means =
**s/√n** - Figure 5.8 on p. 336:

- Example 5.18 on p. 338

- Central Limit Theorem
- Simple random samples of size n from
**any**population with mean μ and finite standard distribution σ. When n is large (typically ≥ 30), the sampling distribution of the sample mean is approximately**Normal**. - Example 5.19 on p. 339

- Simple random samples of size n from
- Video

Activity:

- Test the Central Limit Theorem
- Calculate sample means (use Vehicle Year)
- Report results

Study:

- For practice complete Exercises 5.36, 5.37, 5.38, 5.39 on pp. 336-340
- Read pp. 335-344, Sampling Distribution

Mean | 2007.65 |

Standard Error | 0.63 |

Median | 2006.50 |

Mode | 2013.00 |

Standard Deviation | 5.77 |

Range | 23.00 |

Minimum | 1996.00 |

Maximum | 2019.00 |

Sum | 168643.00 |

Count | 84.00 |

Largest(1) | 2019.00 |

Smallest(1) | 1996.00 |

sampling distribution mean | 2007.65 |

sampling distribution stdev | 0.63 |