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Estimation & Confidence Intervals (Estimation & Confidence…

- - - - Build Confidence Interval around it
        
        σ unknown (t)
        
        σ known (z)
        
        proportion (z)
        
        Considers dispersion, n & α
    - - x̅1 = 100 with range of [5 to 195]
      - x̅2 = 100 with range of [90 to 110]
      - Examples
        
        Titleist
        
        Undergrad
      - Video
  - - - [Point estimate ± Margin of Error]
      - Video
    - - Example
    - - Finding t-value
      - Example
        
        Video
    - - Finding Z-value
      - Example
        
        Video
      - Video
    - - Finding Z-value
      - Example
        
        Video
    - - σ unknown
      - more conservative (wider interval)
      - 2 components: α/2, df

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Estimation & Confidence Intervals

sigma unknown

Estimation & Confidence Intervals

How much confidence in estimate?

Now called "point estimate"

Build Confidence Interval around it

Confidence Intervals

General Formula:

[Point estimate ± Margin of Error]

Inferential Theory

σ unknown (t)

σ known (z)

proportion (z)

Considers dispersion, n & α

Why Care?

x̅1 = 100 with range of [5 to 195]

x̅2 = 100 with range of [90 to 110]

Examples

Titleist

Undergrad

Example

sigma unknown

sigma known

proportion

Finding Z-value

Finding Z-value

Finding t-value

Example

Example

Example

t-distribution

σ unknown

more conservative (wider interval)

2 components: α/2, df

Factors influencing Confidence Interval Width

Factors that influence width

vs.

proportion problem

t distn problem

All Rights Reserved by Brent Marinan & University of Arizona

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