You Are Studying Two Normally Distributed Populations with Equal Variances $\bar { x } _ { 1 }$

question 125

Essay

You are studying two normally distributed populations with equal variances.A random sample is taken from each population.The relevant sample statistics are $\bar { x } _ { 1 }$
= 34.36, $\bar { x } _ { 1 }$
= 26.45,s₁ = 9,s₂ = 6,n₁ = 10,n₂ = 16.Compute a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$
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Definitions:

Hypothetical Syllogism

A logical argument composed of two conditional statements and a conclusion, based if the first premise is true, then the second one follows.

Modus Ponens

A valid form of argument in which if a conditional statement (“if p then q”) and its antecedent (“p”) are true, then the consequent (“q”) is also true.

Modus Tollens

A form of deductive argument that takes the form "If P, then Q. Not Q. Therefore, not P," which is used to derive a conclusion from a hypothesis by negation.

Hypothetical Syllogism

A logical argument consisting of two conditional statements and a conclusion that is logically inferred.