You are performing a hypothesis test of a single population...

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Key Concepts

Normality Assumption

The Student’s t-test for a single population mean assumes that the underlying population from which the sample is drawn is normally distributed. This assumption is crucial, especially when the sample size is small, because the properties of the t-distribution rely on the data following a normal pattern. In large samples, the Central Limit Theorem can mitigate deviations from normality, but for small samples, any significant departures from normality can affect the validity of the test.

Independence of Observations

In addition to assuming normality, it is also essential that the data points are independent of one another. This means that the value of one observation does not influence or correlate with another, ensuring that the variability captured in the sample reflects the true variability of the population. Although this pertains to the sample collection method rather than the data distribution per se, it is a critical assumption in the context of hypothesis testing using the t-distribution.

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