If the variables x and z are so related that z = ax+b for each where a and b are constant, then z = ax+b.

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Option a: True. Solution: Step 1: Recall the property of arithmetic mean under linear transformation. If z = ax + b for every observation, then by the linearity of the arithmetic mean: z-bar = ax-bar + b Step 2: Apply to the given relation. Since z = ax + b holds for each value, the mean z-bar satisfies: z-bar = ax-bar + b This is exactly the statement z-bar = ax-bar + b, which is True. Hence, Option A is the correct answer.

If the variables $\displaystyle x$ and $\displaystyle z$ are so related that $\displaystyle z = ax+b$ for each where $\displaystyle a$ and $\displaystyle b$ are constant, then $\displaystyle z = ax+b$ .

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If the variables x\displaystyle xx and z\displaystyle zz are so related that z=ax+b\displaystyle z = ax+bz=ax+b for each where a\displaystyle aa and b\displaystyle bb are constant, then z=ax+b\displaystyle z = ax+bz=ax+b.