Sign Test for Median of Single Population

In a class of 100 students, 60 scored a grade of less than 45 on a test, 15 scored 45, and 25 scored more than 45.

This simple random data, drawn from a single population, allows for the use of the sign test to examine claims about the scores' median.

The null hypothesis posits that the median equals 45, whereas the alternative hypothesis suggests the median is less than 45.

In this scenario, positive signs are assigned to scores above 45 and negative signs to those below 45.

Given that most scores are below 45, the sample data supports the alternative hypothesis.

Since n — the total number of positive and negative signs — exceeds 25, the test statistic is calculated using z statistic as follows.

For a one-tailed test at a 0.05 confidence level, the critical z-value is -1.645. As the test statistic falls below the critical value, we reject the null hypothesis, suggesting that the dataset's median is less than 45.