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T - Statistic vs. Z-Statistic

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Why is a t-statistic, as opposed to a z-statistic, used to test small populations? When does the t-statistic approximate the z-statistic?

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The solution explains why t-statistic, as opposed to a z-statistic, used to test small populations and when the t-statistic approximates the z-statistic. 262 words with a formula and references.

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t -statistic Vs z-statistic

Why is a t-statistic, as opposed to a z-statistic, used to test small populations?

Answer

According to the central limit theorem, sampling distribution of sample mean follows normal distribution as long as the sample size is sufficiently large. Hence for large samples, if the population standard deviation is known, we can compute z-score and use the normal distribution to test the population.

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