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Summary of Formulas

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Formula 1: General form of a confidence interval

( lower value , upper value ) = ( point estimate - error bound , point estimate + error bound ) (lower value,upper value)=(point estimate-error bound,point estimate+error bound)

Formula 2: To find the error bound when you know the confidence interval

error bound = upper value - point estimate error bound=upper value-point estimate OR error bound = upper value - lower value 2 error bound= upper value - lower value 2

Formula 3: Single Population Mean, Known Standard Deviation, Normal Distribution

Use the Normal Distribution for Means EBM = z α 2 ⋅ σ n EBM= z α 2 ⋅ σ n

The confidence interval has the format ( x¯ - EBM , x¯ + EBM ) ( x -EBM, x +EBM).

Formula 4: Single Population Mean, Unknown Standard Deviation, Student's-t Distribution

Use the Student's-t Distribution with degrees of freedom df = n - 1 df=n-1. EBM = t α 2 ⋅ s n EBM= t α 2 ⋅ s n

Formula 5: Single Population Proportion, Normal Distribution

Use the Normal Distribution for a single population proportion p ' = x n p'= x n

EBP = z α 2 ⋅ p ' ⋅ q ' n p ' + q ' = 1 EBP= z α 2 ⋅ p ' ⋅ q ' n p'+q'=1

The confidence interval has the format ( p ' - EBP , p ' + EBP ) (p'-EBP,p'+EBP).

Formula 6: Point Estimates

x¯ x is a point estimate for μ μ

p ' p' is a point estimate for ρ ρ

s s is a point estimate for σ σ

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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

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| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks