Final answer:
Hypothesis tests are categorized based on the alternative hypothesis into two-tailed, left-tailed, or right-tailed. The random variable is the variable being tested, represented by specific symbols, and the test's distribution may vary depending on sample size and known population parameters.
Step-by-step explanation:
In hypothesis testing within statistics, tests can be classified as either two-tailed, left-tailed, or right-tailed based on the alternative hypothesis (Ha). When Ha contains a not equals (≠) symbol, the test is two-tailed, indicating that the researcher is looking for a difference in either direction from the hypothesized value.
If Ha contains a less-than (<) symbol, it is a left-tailed test, suggesting the researcher expects the parameter to be less than the hypothesized value. Conversely, Ha with a greater-than (>) symbol indicates a right-tailed test, implying the researcher anticipates the parameter to be greater than the hypothesized value.
The random variable for a hypothesis test, often represented by symbols like X, T, or Z, is the variable for which the testing is conducted, such as a sample mean or proportion. The choice between using a normal distribution or a Student's t-distribution for the hypothesis test often depends on the sample size and whether the population standard deviation is known.