Test of Proportions Z

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Presentation Description

The Test of Proportions can be used to infer the probability of the null hypothesis for a sample versus norms design with a variable in a binary nominal scale. It is an estimate of the binomial distribution.

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Presentation Transcript

Test of Proportions : 

Test of Proportions headlessprofessor

When to use : 

When to use Inferential statistic: tests a null hypothesis

When to use : 

When to use Inferential statistic Sample vs. norms design

When to use : 

When to use Inferential statistic Sample vs. norms Binary nominal scale

What you need : 

What you need Sample size Population proportion Sample proportion

Proportion : 

Proportion Part / Whole

Proportion : 

Proportion Part / Whole Percent / 100

Example : 

Example A sample of 64 Hancock’s customers

Example : 

Example A sample of 64 Hancock’s customers Found 57 women and only 7 men.

Example : 

Example N = 64 57 women & 7 men. For a proportion of 57 / 64 = .89

Example : 

Example N = 64 57 women & 7 men. Sample proportion = .89 Population = .50

How to Calculate : 

How to Calculate Ps – Pp --------------------- ((1-Pp) X (Pp / N)) ^.5

How to Calculate : 

How to Calculate Get denominator first and store it in the calculator memory

How to Calculate : 

How to Calculate 1 – population proportion .5 = .5

How to Calculate : 

How to Calculate 1 – population proportion .5 = .5 Times population proportion .50

How to Calculate : 

How to Calculate 1 – population proportion .5 = .5 Times population proportion .50 .5 X .5

How to Calculate : 

How to Calculate Times population proportion .5 .5 X .5 = .25

How to Calculate : 

How to Calculate .5 X .5 = .25 Divide by 64

How to Calculate : 

How to Calculate = .25 Divide by 64 Equals = .0039

How to Calculate : 

How to Calculate = .25 Divide by 64 Equals = .0039 Square root =.0625

How to Calculate : 

How to Calculate equals .0625 That is the denominator

How to Calculate : 

How to Calculate equals .0625 That is the denominator Save it in your memory (don’t round)

How to Calculate : 

How to Calculate Get the numerator

How to Calculate : 

How to Calculate Get the numerator Sample proportion minus population proportion

How to Calculate : 

How to Calculate Get the numerator Sample proportion minus population proportion .89 - .50 = .39

How to Calculate : 

How to Calculate = .39 That is your numerator

How to Calculate : 

How to Calculate = .39 That is your numerator Divide by / Memory recall Equal

How to Calculate : 

How to Calculate = .39 That is your numerator Divide by / Memory recall Equal = 6.24

How to Calculate : 

How to Calculate Equal = 6.24 That is your Z score

How to Calculate : 

How to Calculate Go to your T table Look at last row (infinity)

How significant is this? : 

How significant is this?

How significant is this? : 

How significant is this?

What this means? : 

What this means? There is less than one chance in a thousand that such a sample of 89% female would be drawn randomly from a population of 50% female.

What this means? : 

What this means? Therefore, we should Reject the null hypothesis

Alternative tests : 

Alternative tests Chi Square: Observed = sample Expected = from population

Alternative tests : 

Alternative tests Chi Square Kolomogorov-Smirnov

Alternative tests : 

Alternative tests Chi Square Kolomogorov-Smirnov Binomial Distribution

Test of Proportions : 

Test of Proportions headlessprofessor