7-9-4 Tests

2-Sample Z Test

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Description: Tests a hypothesis relative to the population mean of two populations when the standard deviations of the two populations are known. A 2-Sample Z Test is used for normal distributions.

 

Z =

 

o1 — o2

o1 : sample mean of sample 1 data

 

 

o2 : sample mean of sample 2 data

 

 

 

 

 

 

 

 

 

 

 

2

2

 

 

 

 

 

1

+

2

 

 

 

σ1 : population standard deviation of sample 1

 

 

 

 

 

 

 

 

 

 

n1

n2

σ2 : population standard deviation of sample 2

 

 

 

 

 

 

 

 

 

n1 : size of sample 1

 

 

 

 

 

 

 

 

 

n2 : size of sample 2

Definition of Terms

 

 

 

 

 

 

 

μ1 condition :

population mean value test conditions (“≠” specifies two-tail test,

 

 

 

“<” specifies one-tail test where sample 1 is less than sample 2, “>”

σ1 :

 

 

specifies one-tail test where sample 1 is greater than sample 2).

 

 

population standard deviation of sample 1 (σ1 > 0)

σ2 :

 

 

population standard deviation of sample 2 (σ2 > 0)

List(1) :

 

 

list where sample 1 data is located

List(2) :

 

 

list where sample 2 data is located

Freq(1) :

frequency of sample 1 (1 or list name)

Freq(2) :

frequency of sample 2 (1 or list name)

o1 :

 

 

sample mean of sample 1 data

n1 :

 

 

size of sample 1 (positive integer)

o2 :

 

 

sample mean of sample 2 data

n2 :

 

 

size of sample 2 (positive integer)

Calculation Result Output

 

 

 

 

 

μ1 ≠ μ2: test condition

 

z:

z value

 

 

 

 

 

p:

p-value

 

 

 

 

 

o1:

sample mean of sample 1 data

o2:

sample mean of sample 2 data

x1σn−1: sample standard deviation of sample 1 (Displayed only for list format.)

x2σn−1: sample standard deviation of sample 2 (Displayed only for list format.)

n1:

size of sample 1

 

n2:

size of sample 2

 

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