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

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

H0:  μ1 - μ2 = 0
Ha:  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 0.707107

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 0.00126263

DF = 198, rounded to an integer is 198

DF = 198, rounded to an integer is 198
##### How does the Confidence Interval/Hypothesis Testing for the Difference of Means Calculator work?
Free Confidence Interval/Hypothesis Testing for the Difference of Means Calculator - Given two large or two small distriutions, this will determine a (90-99)% estimation of confidence interval for the difference of means for small or large sample populations.
Also performs hypothesis testing including standard error calculation.
This calculator has 7 inputs.

### What 2 formulas are used for the Confidence Interval/Hypothesis Testing for the Difference of Means Calculator?

α = 1 - Confidence%
(x1 - x2) - zscoreα x √a < μ1 - μ2 < (x1 - x2) + zscoreα x √a

For more math formulas, check out our Formula Dossier

### What 7 concepts are covered in the Confidence Interval/Hypothesis Testing for the Difference of Means Calculator?

alternative hypothesis
opposite of null hypothesis. One of the proposed proposition in the hypothesis test.
H1
confidence interval
a range of values so defined that there is a specified probability that the value of a parameter lies within it.
confidence interval/hypothesis testing for the difference of means
hypothesis testing
statistical test using a statement of a possible explanation for some conclusions
mean
A statistical measurement also known as the average
null hypothesis
in a statistical test, the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.
H0
standard error
measures how far the sample mean (average) of the data is likely to be from the true population mean
SE = σ/√n