Casio FX-9860G t, C, df, n1 + n2 –, df = n1 + n2 –, u 2-Sample t Test

6-5-13 Tests

u 2-Sample t Test

2-Samplet Test compares the population means when the population standard deviations are unknown. The 2-Samplet Test is applied to t-distribution.

The following applies when pooling is in effect.

t =			o1 – o2
			1			1
	xpσn–12					+
					n1		n2
xpσn–1		=		(n1–1)x1σn–12+(n2–1)x2σn–12
							n1 + n2 – 2

df = n1 + n2 – 2

The following applies when pooling is not in effect.

t =	o1 – o2
	x1σ n–12		x2σn–12
		+
	n1		n2

df =		1
	C2			(1–C)2
			+
	n1–1				n2–1
		x1σ n–12
C =				n1
	x1σn–12				x2σn–12
	n1			+	n2

x¯1 : mean of sample 1

x¯2 : mean of sample 2 x1σn-1 : standard deviation of

sample 1

x2σn-1 : standard deviation of sample 2

n1 : size of sample 1

n2 : size of sample 2

xpσn-1 : pooled sample standard deviation

df : degrees of freedom

x¯1 : mean of sample 1

x¯2 : mean of sample 2 x1σn-1 : standard deviation of

sample 1

x2σn-1 : standard deviation of sample 2

n1 : size of sample 1

n2 : size of sample 2

df : degrees of freedom

Perform the following key operations from the statistical data list.

3(TEST)

2(t)

2(2-S)

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