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Which assumptions a z-test for a mean needs

Question

Rishab plans a z-test about a population mean. Which of these conditions are required?

(1) the population variance is known;

(2) the data form a random sample from the population;

(3) the sample mean is approximately normally distributed;

(4) at least 3030 observations are collected.

Give the required condition numbers in increasing order as one number (e.g. 2424 for conditions 2 and 4).

Short answer

123123. A z-test needs a known (or reliably estimated) variance, a random sample, and an approximately normal sample mean. The n≥30n\ge30 rule is only a heuristic for getting normality via the CLT; if the population is itself normal, any nn works.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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