# AP Statistics Curriculum 2007 Estim Var

(Difference between revisions)
 Revision as of 18:59, 14 June 2007 (view source)IvoDinov (Talk | contribs)← Older edit Revision as of 16:51, 4 February 2008 (view source)IvoDinov (Talk | contribs) Newer edit → Line 1: Line 1: ==[[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== + + 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=== - Example on how to attach images to Wiki documents in included below (this needs to be replaced by an appropriate figure for this section)! + The most unbiased point estimate for the population variance \sigma&^2[/itex] is the [[AP_Statistics_Curriculum_2007_EDA_Var | sample-variance  (s2)]] and the point estimate for the population standard deviation [itex]\sigma is the [[AP_Statistics_Curriculum_2007_EDA_Var | sample standard deviation (s)]]. -
[[Image:AP_Statistics_Curriculum_2007_IntroVar_Dinov_061407_Fig1.png|500px]]
+ + 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===

## 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  (s2) 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.

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### Model Validation

Checking/affirming underlying assumptions.

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### Examples

Computer simulations and real observed data.

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### Hands-on activities

Step-by-step practice problems.

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