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
Find α spread range:
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
You have 2 free calculationss remaining
What this means is if we repeated experiments, the proportion of such intervals that contain μ1 - μ2 would be 90%
What is the Answer?
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.
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
(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
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