Teste t (1 amostra)

The one-sample t-test compares a sample mean to a known population value to assess statistical significance. It calculates a t-statistic using the formula t = (x̄ - μ₀)/(s/√n), where x̄ is the sample mean, μ₀ is the hypothesized value, s is the sample standard deviation, and n is the sample size. This t-value is then compared to a t-distribution to determine significance.

This test is particularly useful when the population standard deviation is unknown and the sample size is small (typically n < 30). The t-distribution accounts for the additional uncertainty in small samples by having heavier tails than the normal distribution. The formula adjusts for sample variability and size to quantify the observed difference.

Key assumptions include: 1) Random and representative sampling; 2) Normality of the data distribution, especially critical for small samples; 3) For large samples (n ≥ 30), the z-test may be more appropriate due to the Central Limit Theorem. Normality checks are recommended before applying the test.

If data violates normality assumptions, non-parametric alternatives like the Wilcoxon signed-rank test can be used. The test output includes a p-value indicating the probability of observing the data under the null hypothesis. A low p-value (< 0.05) typically rejects the null hypothesis.