Hypothesis Testing 101 - StatsMonkey.

[Pages:3]Hypothesis Testing 101

Type of Sampling Distribution

Center

One Mean

x = x

One Proportion

p^ = p

Difference between 2 independent sample

means

x = x1 - x2

Difference between 2 independent sample proportions

p^1- p^2 = p1 - p2

Spread Shape

2x

=

2x n2

x

=

x n

2 p^

=

p(1 - n

p)

p^ =

p(1- p) n

IF n is sufficiently large, THEN sampling distribution of sample mean will be approximately normally distributed, no matter the shape of parent population distribution.

IF np 10 AND n(1 - p) 10, THEN sampling distribution will be approximately normally distributed.

2x

=

2 x1

n1

+ 2x2 n2

x =

2 1

+

2 2

n1 n2

IF n is sufficiently large, THEN sampling distribution of difference between two independent sample means will be approximately normally distributed.

2 p^1 - p^2

=

p1 (1 - n1

p1) +

p2 (1- n2

p2 )

= p^1 - p^2

p1(1- p1) + p2 (1- p2 )

n1

n2

IF

n1 p1 10, n1(1- p1) 10, n2 p2 10,

and n2 (1- p2 ) 10

THEN sampling distribution of difference between two independent sample proportions will be approximately normally distributed.

Assumptions &

Conditions

1. Random sample of observations

2. Independent observations 3. 10n < N 4. Must be roughly normal if

is not known and/or n is

small

1. Random sample of observations

2. Independent observations

3. 10n < N 4. np 10, nq 10

1. Random samples of

1. Random samples of observations

observations from two

from two independent populations

independent populations 2. Independent observations

2. Independent observations 3. 10n < N

3. 10n < N

Hypothesis Testing 101 z-test if is known & n > 40 ish

t-test if is not known and/or n is small

Tests

One Proportion z-Test ?

Intervals

statistic - parameter

z =

SE

b g z = p - 1- n

1-prop z-test

z = obs - exp = pl - p

SE

pl

b g b g z = x1 - x 2 - 1 - 2

2 1

+

2 2

n1 n2

if 's are known

One Proportion zInterval ? sample statistic ?

critical value *

standard deviation

b g b g t = x1 - x 2 - 1 - 2

s

2 1

+

s

2 2

n1 n2

if 's are not known

b g x1 - x2

?

t

* df

s

2 1

+

s

2 2

n1 n2

b g p ? z*

p 1- p n

b g z = ( p1 - p2 ) - 1 - 2

b gFHG IKJ pc 1- pc

1+ 1 n1 n2

p^c

= n1 p^1 n1

+ n2 p^2 + n2

= combined _ successes combined _ sample _ size

c h c h ( p1 - p2 ) ? z *

p1 1 - p 2 + p 2 1 - p 2

n1

n2

If we don't know

x - we estimate it with

s ? we estimate it with x

p() ? we estimate it with p^

If we use these estimates to calculate the variability for a sampling

distribution, we now call that the standard error.

So... If SD: ( p^ ) = p(1- p)

n

Then the SE: ( p^ ) = p^ (1- p^ )

n

And...If SD ( x ) = X

n

Then the SE ( x ) = sx

n

Hypothesis Testing 101

H: Hypotheses

State in symbols and in words

C: Conditions

Independent Random Large enough Success/Failure

Be sure to state if you are able to use the Normal model or not!

T: Test statistic

Write the entire formula with correct symbols, including degrees of freedom (df) or name that test! Evaluate the test statistic by writing in the values and having the calculator produce the numbers (including possibly, df's)

State "by calculator" in your answer

A: Alpha

Compare p-level to alpha, include a properly labeled sketch.

C: Conclude:

Cite the comparison of p-level to alpha AND state conclusion in context.

I: Introduce

A full sentence identifying the parameter in context and in symbol:

? "I am creating a 99% confidence interval for , the mean radon level in ppm in houses in Anytown."

C: Conditions

List and check conditions as needed, including random sample, n < .1N, and evidence of normality if needed

? (np & nq are at least ten, etc., or boxplot checked for symmetry, or n large, whatever your text asks)

F: Formula

Write the entire formula with correct symbols, including df

C: Calculations

Write in the values, including the z- or t - critical value. Have

the calculator produce the interval. State "by calculator" in your answer

I: Interpret.

Two sentences:

? one for the numbers in context

o I am 99% confident that the true mean radon levels in ppm lies in the interval between ___ and ___

? one for the method

o 99% of similiarly constructed intervals will contain the true mean.

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