Null hypothesis: μ ≥ 50. Alternative hypothesis: μ < 50. Test for evidence using data and significance level.
The null hypothesis, denoted as H0, represents the default assumption in a statistical test. In this case, the null hypothesis is written as H0: μ ≥ 50, where μ is the population mean. The symbol "≥" indicates greater than or equal to. Therefore, the null hypothesis posits that the population mean is greater than or equal to 50.
When testing whether the mean is less than 50, the alternative hypothesis (denoted as H1 or Ha) would be written as H1: μ < 50, indicating that there is evidence to suggest the population mean is less than 50.
Statistical hypothesis testing involves collecting and analyzing data to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. The decision is often based on the p-value, which represents the probability of obtaining results as extreme as the observed data under the assumption that the null hypothesis is true. If the p-value is sufficiently small (typically below a predetermined significance level, such as 0.05), one may reject the null hypothesis in favor of the alternative, suggesting that there is evidence to support the claim that the mean is less than 50.
It's important to note that the formulation of the null and alternative hypotheses is crucial in guiding the statistical analysis and interpretation of the results.