A Statistician Wants to Test for the Equality of Means

question 23

Essay

A statistician wants to test for the equality of means in two independent samples drawn from normal populations. However, he will not perform the equal-variance t-test of the difference between the population means if the condition necessary for its use is not satisfied. The data are as follows: $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | l | } \hline \text { Sample 1: } & 7 & 9 & 6 & 15 & 7 & 10 & 8 & 12 & & \\\hline \text { Sample 2: } & 2 & 25 & 9 & 15 & 10 & 18 & 5 & 22 & 27 & 3 \\\hline\end{array}$$ Given the data above, can the statistician conclude at the 5% significance level that the required condition is not satisfied?

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Definitions:

Performance Advantage

The superior capability or efficiency demonstrated by an individual or system in executing a task compared to others.

Research Methods

Various strategies, techniques, and tools used to investigate questions and hypotheses in the scientific field.

Empirical Data

Information acquired by observation or experimentation that is used as a basis for knowledge creation or validation.

Scientific Method

The scientific method is a systematic process for conducting research and experimentation, involving observation, hypothesis formulation, experimentation, and conclusion to test scientific theories.