If Two Random Samples of Sizes N₁ and N₂ Are $\bar { X } _ { 1 } - \bar { X } _ { 2 }$

question 97

Multiple Choice

If two random samples of sizes n₁ and n₂ are selected independently from two non-normally distributed populations,then the sampling distribution of the sample mean difference, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ ,is

• A) always non-normal
• B) always normal
• C) approximately normal only if n₁ and n₂ are both larger than or equal to 30
• D) approximately normal regardless of n₁ and n₂

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Definitions:

Parsimonious

A term used to describe a theory or explanation that is simple and lacks unnecessary elements, favoring minimal assumptions.

Replicable

Capable of being duplicated or repeated under the same conditions, allowing for verification of results in scientific research.

Statistical

Related to or based on the use of statistics, involving the collection, analysis, interpretation, and presentation of numerical data.

Double-blind

A study design in which neither the participants nor the experimenters know who is receiving a particular treatment, thereby eliminating bias.