1 / 15

Sampling Distribution of a Sample Proportion

Sampling Distribution of a Sample Proportion. Lecture 26 Sections 8.1 – 8.2 Fri, Oct 12, 2007. Preview of the Central Limit Theorem. We looked at the distribution of the average of 1, 2, and 3 uniform random variables U (0, 1).

kato
Download Presentation

Sampling Distribution of a Sample Proportion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Sampling Distribution of a Sample Proportion Lecture 26 Sections 8.1 – 8.2 Fri, Oct 12, 2007

  2. Preview of the Central Limit Theorem • We looked at the distribution of the average of 1, 2, and 3 uniform random variables U(0, 1). • We saw that the shapes of their distributions was moving towards the shape of the normal distribution.

  3. Preview of the Central Limit Theorem 2 1 0 1

  4. Preview of the Central Limit Theorem 2 1 0 1

  5. Preview of the Central Limit Theorem 2 1 0 1

  6. Preview of the Central Limit Theorem • Some observations: • Each distribution is centered at the same place, ½. • The distributions are being “drawn in” towards the center. • That means that their standard deviation is decreasing. • Can we quantify this?

  7. Preview of the Central Limit Theorem • = ½ 2 = 1/12 2 1 0 1

  8. Preview of the Central Limit Theorem • = ½ 2 = 1/24 2 1 0 1

  9. Preview of the Central Limit Theorem • = ½ 2 = 1/36 2 1 0 1

  10. Preview of the Central Limit Theorem • This tells us that a mean based on three observations is much more likely to be close to the population mean than is a mean based on only one or two observations.

  11. Parameters and Statistics • THE PURPOSE OF A SAMPLE STATISTIC IS TO ESTIMATE A POPULATION PARAMETER. • A sample mean is used to estimate the population mean. • A sample proportion is used to estimate the population proportion.

  12. Parameters and Statistics • Sample statistics are variable. • Population parameters are fixed.

  13. Some Questions • We hope that the sample proportion is close to the population proportion. • How close can we expect it to be? • Would it be worth it to collect a larger sample? • If the sample were larger, we would expect the sample proportion to be closer to the population proportion. • How much closer? And how much larger?

  14. Experiment • Survey finds drop in hand hygiene

  15. Experiment

More Related