Perform a hypothesis test, enter a test median, and select the alternative hypothesis.
Use this one-sided test to determine whether the population median is less than the test median, and get an upper bound. This one-sided test gives greater power, it cannot detect when the population median is greater.
For example, a researcher uses this one-sided test to determine whether the median time that it takes a drug to relieve symptoms is less than 12 minutes. This one-sided test has greater power to determine whether the median is less than 12, but it cannot detect whether the median is greater than 12.
Use this two-sided test to determine whether the population median differs from the test median, and to get a two-sided confidence interval. A two-sided test can detect differences that are less than or greater than the hypothesized value, but it has less power than a one-sided test.
For example, an inspector tests whether the median chromium content in stainless steel differs from the specification of 0.18. Because any difference from the specification is important, the inspector uses this two-sided test to determine whether the median is greater than or less than the specification.
Use this one-sided test to determine whether the population median is greater than the test median and get a lower bound. This one-sided test gives greater power, it cannot detect when the population median is less than the test median.
For example, a hospital administrator uses this one-sided test to determine whether the median patient satisfaction rating is greater than 90. This one-sided test has greater power to determine whether the median is greater than 90, but it cannot determine whether the median is less than 90.