Sample size allocation. Suppose we are testing the hypotheses
H0:μ1 = μ2
H1:μ1 not equal μ2

where σ12 and σ22 are known. Resources are limited, and consequently the total sample size n1 + n2 = N. How should we allocate the N observations between the two populations to obtain the most powerful test?

The test statistic

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

Here

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc