Assume that you have a sample of n 1 equals 8n1=8, with the sample mean upper x overbar 1 equals 42x1=42, and a sample standard deviation of upper s 1 equals 4s1=4, and you have an independent sample of n 2 equals 15n2=15 from another population with a sample mean of upper x overbar 2 equals 34x2=34 and a sample standard deviation of upper s 2 equals 5s2=5. what assumptions about the two populations are necessary in order to perform thepooled-variance t test for the hypothesis upper h 0 : μ 1 equals μ 2h0: μ1=μ2 against the alternative upper h 1 : μ 1 > μ 2h1: μ1> μ2 and make a statistical decision?

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Step-by-step explanation:

Hello!

To make a pooled variance t-test you have to make the following assumptions:

The study variables X₁ and X₂ must be independent.

Both variables should have a normal distribution, X₁~N(μ₁; σ₁²) and X₂~N(μ₂; σ₂²)

The population variances should be equal but unknown, σ₁² = σ₂² = ?.

You have the information of two samples:

Sample 1

n₁=8

sample mean X[bar]₁= 42

sample standard deviation S₁=4

Sample 2

n₂=15

sample mean X[bar]₂= 34

sample standard deviation S₂= 5

For the hypothesis:

H₀: μ₁ = μ₂

H₁: μ₁ > μ₂

The statistic is:

t=  (X[bar]₁ - X[bar]₂) - (μ₁ - μ₂) ~

Sa

Sa²=

Sa²= 22

Sa= 4.69

= 3.8962 ≅ 3.9

The critical region is one-tailed, for example for α: 0.05

Since > 1.721, then the decision is to reject the null hypothesis.

I hope it helps!

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