To begin, ensure your dataset meets the basic conditions for testing: random sampling, a normal distribution of data, and an interval or ratio scale. Once these are confirmed, proceed by stating your null hypothesis, typically asserting no difference between the sample mean and a given population mean.
Next, calculate the test statistic using the formula: t = (X̄ – μ) / (s / √n), where X̄ is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size. After finding the t-value, compare it with the critical value from the t-distribution table, based on your chosen significance level (usually 0.05) and degrees of freedom (n – 1).
If your calculated t-value exceeds the critical value, reject the null hypothesis. Otherwise, retain it. This process allows you to make data-driven conclusions about whether the sample mean significantly differs from the hypothesized population mean.