# AP Statistics Curriculum 2007 Estim Proportion

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=== Estimating a Population Proportion=== | === Estimating a Population Proportion=== | ||

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- | == | + | When the sample size is large, the sampling distribution of the sample proportion <math>\hat{p}</math> is approximately Normal, by [[AP_Statistics_Curriculum_2007_Limits_CLT |CLT]], as the sample proportion may be presented as a [[AP_Statistics_Curriculum_2007_Limits_Norm2Bin |sample average or Bernoulli random variables]]. When the sample size is small, the normal approximation may be inadequate. To accommodate this we will modify <math>\hat{p}</math> slightly |

- | + | : <math>\hat{p}={y\over n} \longrightarrow \tilde{y}={y+0.5z_{\alpha \over 2}^2 \over n+z_{\alpha \over 2}^2},</math> | |

+ | where [[AP_Statistics_Curriculum_2007_Normal_Critical | <math>z_{\alpha \over 2}</math> is the normal critical value we saw earlier]]. | ||

- | + | The standard error of <math>\hat{p}</math> also needs a slight modification | |

+ | : <math>SE_{\hat{p}} = \sqrt{\hat{p}(1-\hat{p})\over n} \longrightarrow SE_{\tilde{p}} = \sqrt{\tilde{p}(1-\tilde{p})\over n+z_{\alpha \over 2}^2}.</math> | ||

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+ | ===Confidence intervals for proportions=== | ||

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+ | The confidence intervals for the sample proportion <math>\hat{p}</math> and the corrected-sample-proportion <math>\tilde{p}</math> are given by | ||

+ | : <math>\hat{p}\pm z_{\alpha\over 2} SE_{\hat{p}}</math> | ||

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+ | :<math>\tilde{p}\pm z_{\alpha\over 2} SE_{\tilde{p}}</math> | ||

===Model Validation=== | ===Model Validation=== |

## Revision as of 05:09, 4 February 2008

## Contents |

## General Advance-Placement (AP) Statistics Curriculum - Estimating a Population Proportion

### Estimating a Population Proportion

When the sample size is large, the sampling distribution of the sample proportion is approximately Normal, by CLT, as the sample proportion may be presented as a sample average or Bernoulli random variables. When the sample size is small, the normal approximation may be inadequate. To accommodate this we will modify slightly

where is the normal critical value we saw earlier.

The standard error of also needs a slight modification

### Confidence intervals for proportions

The confidence intervals for the sample proportion and the corrected-sample-proportion are given by

### Model Validation

Checking/affirming underlying assumptions.

- TBD

### Computational Resources: Internet-based SOCR Tools

- TBD

### Examples

Computer simulations and real observed data.

- TBD

### Hands-on activities

Step-by-step practice problems.

- TBD

### References

- TBD

- SOCR Home page: http://www.socr.ucla.edu

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