Problem

Determine whether the following statement is true or false:
We use a $t$ distribution when we don't know $\sigma$ and a $z$ distribution when we do.
True
False
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Answer

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Answer

Final Answer: \(\boxed{True}\)

Steps

Step 1 :The question is asking about the conditions under which we use a t-distribution and a z-distribution in statistics.

Step 2 :The t-distribution is typically used when the population standard deviation (σ) is unknown and the sample size is small.

Step 3 :The z-distribution, on the other hand, is used when the population standard deviation is known or the sample size is large.

Step 4 :Therefore, the statement is true.

Step 5 :Final Answer: \(\boxed{True}\)

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