# AP Statistics Curriculum 2007 Estim Var

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==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Estimating Population Variance== | ==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Estimating Population Variance== | ||

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+ | In manufacturing, and many other fields, controlling the amount of variance in producing machinery parts is very important. It is important that the parts vary little or not at all. | ||

=== Estimating Population Variance and Standard Deviation=== | === Estimating Population Variance and Standard Deviation=== | ||

- | + | The most unbiased point estimate for the population variance <math>\sigma&^2</math> is the [[AP_Statistics_Curriculum_2007_EDA_Var | sample-variance (s<sup>2</sup>)]] and the point estimate for the population standard deviation <math>\sigma</math> is the [[AP_Statistics_Curriculum_2007_EDA_Var | sample standard deviation (s)]]. | |

- | < | + | |

+ | We use a [http://en.wikipedia.org/wiki/Chi_square_distribution Chi-square distribution] to construct confidence intervals for the variance and standard distribution. If the random variable has a normal distribution, then the chi-square distribution is: | ||

+ | . | ||

+ | Properties: | ||

+ | 1. All chi-squares values are greater than or equal to zero. | ||

+ | 2. The chi-square distribution is a family of curves, each determined by the degrees of freedom. To form a confidence interval for , use the -distribution with degrees of freedom equal to one less than the sample size. | ||

+ | |||

+ | 3. The area under each curve of the chi-square distribution equals one. | ||

+ | 4. Chi-square distributions are positively skewed. | ||

+ | |||

===Approach=== | ===Approach=== |

## Revision as of 16:49, 4 February 2008

## Contents |

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

In manufacturing, and many other fields, controlling the amount of variance in producing machinery parts is very important. It is important that the parts vary little or not at all.

### Estimating Population Variance and Standard Deviation

The most unbiased point estimate for the population variance **Failed to parse (syntax error): \sigma&^2**

is the sample-variance (s^{2}) and the point estimate for the population standard deviation σ is the sample standard deviation (s).

We use a Chi-square distribution to construct confidence intervals for the variance and standard distribution. If the random variable has a normal distribution, then the chi-square distribution is: . Properties: 1. All chi-squares values are greater than or equal to zero. 2. The chi-square distribution is a family of curves, each determined by the degrees of freedom. To form a confidence interval for , use the -distribution with degrees of freedom equal to one less than the sample size.

3. The area under each curve of the chi-square distribution equals one. 4. Chi-square distributions are positively skewed.

### Approach

Models & strategies for solving the problem, data understanding & inference.

- TBD

### 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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