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

A large sample of 40 units has a mean 5.22 and a standard deviation σ of 2.31
Another large sample of 40 related units has a mean 4.44 and a standard deviation σ of 1.74
Construct a 90% confidence interval for the difference between the means μ1 - μ2

Confidence Interval Formula for μ1 - μ2 is as follows:
(x1 - x2) - zscoreα x √a < μ1 - μ2 < (x1 - x2) + zscoreα x √a where:
x1 = sample mean 1, x2 = sample mean 2, s = sample standard deviation, zscore = Normal distribution Z-score from a probability where α = (1 - Confidence Percentage)/2
and a is denoted below
 σ12 n1
 +
 σ22 n2

Calculate α:
α = 1 - Confidence%
α = 1 - 0.9
α = 0.45726633377059

α = ½(α)
α = ½(0.45726633377059)
α = 0.05

Find z-score for α value for 0.05
zscore0.05 = 1.645 <--- Value can be found on Excel using =NORMSINV(0.95)

## Calculate a:

 √2.312 √40
 +
 √1.742 √40

 √5.3361 √40
 +
 √3.0276 √40

a = √0.1334025 + 0.07569
a = √0.2090925
a = 0.45726633377059

Calculate high end confidence interval total:
High End = (x1 - x2) + zscoreα x √a
High End = (5.22 - 4.44) + 1.645 x 0.45726633377059
High End = 0.78 + 0.75220311905263
High End = 1.5322

Calculate low end confidence interval total:
Low End = (x1 - x2) - zscoreα x √a
Low End = (5.22 - 4.44) - 1.645 x 0.45726633377059
Low End = 0.78 - 0.75220311905263
Low End = 0.0278

Now we have everything, display our 90% confidence interval:
0.0278 < μ1 - μ2 < 1.5322
0.0278 < μ1 - μ2 < 1.5322

What this means is if we repeated experiments, the proportion of such intervals that contain μ1 - μ2 would be 90%

0.0278 < μ1 - μ2 < 1.5322
##### 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