Enter n1	Enter X1	Enter σ1	Enter n2	Enter X2	Enter σ2	Enter Confidence %

   

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A small sample of 100 units has a mean 70 and a standard deviation σ of 5
Another small sample of 100 related units has a mean 65 and a standard deviation σ of 5
Perform a hypothesis test with α = 99

State Hypothesis:

H₀:  μ₁ - μ₂ = 0
H_a:  μ₁ - μ₂ ≠ 0

Calculate Standard Error (SE):

SE = √s₁²/n₁ + s₂²/n₂
SE = √5²/100 + 5²/100
SE = √25/100 + 25/100
SE = √0.25 + 0.25
SE = √0.5
SE = 0.70710678118655

Calculate Test Statistic:

t  =	X1 - X2
	SE

t  =	70 - 65
	0.70710678118655

t  =	5
	0.70710678118655

t = 7.0710678118655

Calculate degrees of freedom:

DF  =	(s12/n1 + s22/n2)2
	(s12/n1)2/(n1 - 1) + (s22/n2)2/(n2 - 1)

DF  =	(52/100 + 52/100)2
	(52/100)2/(100 - 1) + (52/100)2/(100 - 1)

DF  =	(25/100 + 25/100)2
	(25/100)2/99 + (25/100)2/99

DF  =	(0.25 + 0.25)2
	(0.25)2/99 + (0.25)2/99

DF  =	(0.5)2
	0.0625/99 + 0.0625/99

DF  =	0.25
	0.00063131313131313 + 0.00063131313131313

DF  =	0.25
	0.0012626262626263