Intervalo Confiança (t)

The t-Confidence Interval is a statistical tool used to estimate the population mean when the sample is small or when the population variance is unknown. The formula x̄ ± t_(α/2, n-1)·(s/√n) is used, where x̄ is the sample mean, t is the critical value from the t-Student distribution with n-1 degrees of freedom and significance level α, s is the sample standard deviation, and n is the sample size.

The t-Student distribution is used when the population does not follow a normal distribution or when the sample size is small. The critical value t_(α/2, n-1) is obtained from the t-Student table or using statistical software. It is important to note that as the sample size increases, the t distribution approaches the normal distribution.

The t-Confidence Interval is commonly used in research and studies involving small or medium samples. For example, a researcher may use this tool to estimate the mean height of a population based on a sample of 20 individuals. However, it is essential to consider common precautions, such as ensuring the sample is representative of the population and that data are collected accurately.

When interpreting the results of the t-Confidence Interval, it is essential to consider the margin of error and the confidence level. A 95% confidence interval, for instance, means that there is a 95% probability that the population mean lies within the calculated interval. This helps make informed decisions based on the data.