## Content

# t-test

Now we’ll move on to a different statistical test. To compare the average height of students in the class to the average height of students in the entire school, a t-test is required. A t-test is used when the sample size is smaller than 30, the population standard deviation is unknown, and data points are normally distributed. Because the sample of the class has only nine students, this test is appropriate. The first step of the test is to state the null and alternative hypotheses. Again, these are the statements that we will be comparing to each other to determine which one is correct. This test ultimately seeks to determine if there is any statistically significant difference between the average height of the class and the school, not necessarily greater or lower.

H_{0}: There is no statistically significant difference between the average height of students in the class and the average height of students in the school

H_{0}: average height of students in the class = average height of students in the school

H_{0}: μ = μ_{0}

H_{a}: There is a statistically significant difference between the average height of students in the class and the average height of students in the school

H_{a}: average height of students in the class ≠ average height of students in the school

H_{a}: μ ≠ μ_{0}