Confidence Interval/Hypothesis Testing for the Difference of Means Cal

Publish date: 2024-07-18
Confidence Interval/Hypothesis Testing for the Difference of Means Cal MathCelebrity logo Image to Crop 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 4.29 and a standard deviation σ of 1.58
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


Calculate α:
α = 1 - Confidence%
α = 1 - 0.9
α = 0.44250706209054

Find α spread range:
α = ½(α)
α = ½(0.44250706209054)
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
√1.582
√40

√5.3361
√40
√2.4964
√40

a = √0.1334025 + 0.06241
a = √0.1958125
a = 0.44250706209054

Calculate high end confidence interval total:
High End = (x1 - x2) + zscoreα x √a
High End = (5.22 - 4.29) + 1.645 x 0.44250706209054
High End = 0.93 + 0.72792411713894
High End = 1.6579

Calculate low end confidence interval total:
Low End = (x1 - x2) - zscoreα x √a
Low End = (5.22 - 4.29) - 1.645 x 0.44250706209054
Low End = 0.93 - 0.72792411713894
Low End = 0.2021

Now we have everything, display our 90% confidence interval:
0.2021 < μ1 - μ2 < 1.6579

0.2021 < μ1 - μ2 < 1.6579

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

What is the Answer?

0.2021 < μ1 - μ2 < 1.6579

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 hypothesisopposite of null hypothesis. One of the proposed proposition in the hypothesis test.
H1confidence intervala 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 meanshypothesis testingstatistical test using a statement of a possible explanation for some conclusionsmeanA statistical measurement also known as the averagenull hypothesisin a statistical test, the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.
H0standard errormeasures 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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