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tzartiger12

15.04.2022

Mathematics

The test statistic

$Z = \frac{x^{-} _{1}-x^{-} _{2} }{\sqrt{\frac{'σ^2_{1} }{n_{1} } +\frac{'σ^2_{2} '}{n_{2} } } }$

Step-by-step explanation:

Explanation:-

Let x₁⁻ be the mean of the sample of size n₁ from a population mean μ₁ and standard deviation 'σ₁

Let x₂⁻ be the mean of the sample of size n₂ from a population mean μ₂ and standard deviation 'σ₂'

Null hypothesis : H0:μ₁ = μ₂

Alternative hypothesis : H1:μ₁ ≠μ₂

To test whether there is any significant difference between x₁⁻ and x₂⁻ we have use test statistic

$Z = \frac{x^{-} _{1}-x^{-} _{2} }{\sqrt{\frac{'σ^2_{1} }{n_{1} } +\frac{'σ^2_{2} '}{n_{2} } } }$

Here

x₁⁻ be the mean of the first sample x₂⁻ be the mean of the second sample 'σ₁' be standard deviation first population.'σ₂' be standard deviation second population.

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