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 μ

_{1} - μ

_{2} __Confidence Interval Formula for μ___{1} - μ_{2} is as follows:(

x_{1} -

x_{2}) - zscore

_{α} x √

a < μ

_{1} - μ

_{2} < (

x_{1} -

x_{2}) + zscore

_{α} x √

a where:

x_{1} = sample mean 1,

x_{2} = 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

__Calculate α:__ α = 1 - Confidence%

α = 1 - 0.9

α = 0.45726633377059

__Find α spread range:__ α = ½(α)

α = ½(0.45726633377059)

α = 0.05

Find z-score for α value for 0.05

zscore

_{0.05} = 1.645 <--- Value can be found on Excel using =NORMSINV(0.95)

## Calculate a:

a = √

0.1334025 + 0.07569a = √

0.2090925a = 0.45726633377059

__Calculate high end confidence interval total:__ High End = (

x_{1} -

x_{2}) + zscore

_{α} x √

aHigh 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 = (

x_{1} -

x_{2}) - zscore

_{α} x √

aLow 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 < μ**_{1} - μ_{2} < 1.53220.0278 < μ_{1} - μ_{2} < 1.5322

What this means is if we repeated experiments, the proportion of such intervals that contain μ

_{1} - μ

_{2} would be 90%

##### What is the Answer?

0.0278 < μ_{1} - μ_{2} < 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) - zscore

_{α} x √a < μ1 - μ2 < (x1 - x2) + zscore

_{α} 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.

H_{1} - 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.

H_{0} - standard error
- measures how far the sample mean (average) of the data is likely to be from the true population mean

SE = σ/√n

## Tags:

Add This Calculator To Your Website