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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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