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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). - We saw that the shapes of their distributions was

moving towards the shape of the normal

distribution.

Preview of the Central Limit Theorem

2

1

0

1

Preview of the Central Limit Theorem

2

1

0

1

Preview of the Central Limit Theorem

2

1

0

1

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?

Preview of the Central Limit Theorem

2

- ½
- ?2 1/12

1

0

1

Preview of the Central Limit Theorem

2

- ½
- ?2 1/24

1

0

1

Preview of the Central Limit Theorem

2

- ½
- ?2 1/36

1

0

1

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.

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.

Parameters and Statistics

- Sample statistics are variable.
- Population parameters are fixed.

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?

Experiment

- Survey finds drop in hand hygiene

Experiment

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For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

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