7-9-4 Tests

2-Sample Z Test

Menu: [Test]-[Two-Sample ZTest]

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 =

 

 

M1 — M2

M1 : sample mean of sample 1 data

 

 

M2 : 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 (“ξ” specifies two-tail test,

 

 

 

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

 

 

 

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

σ1 :

 

 

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)

M1 :

 

 

sample mean of sample 1 data

n1 :

 

 

size of sample 1 (positive integer)

M2 :

 

 

sample mean of sample 2 data

n2 :

 

 

size of sample 2 (positive integer)

Calculation Result Output

μ1 ξ μ2: test condition

z: p:

M1: M2:

sx1: sx2:

n1: n2:

zvalue p-value

sample mean of sample 1 data sample mean of sample 2 data

sample standard deviation of sample 1 (Displayed only for list format.) sample standard deviation of sample 2 (Displayed only for list format.) size of sample 1

size of sample 2

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