FAQ: Hypothesis Testing: Associations - Introduction

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This community-built FAQ covers the “Introduction” exercise from the lesson “Hypothesis Testing: Associations”.

Paths and Courses
This exercise can be found in the following Codecademy content:

Data Scientist: Machine Learning Specialist
Master Statistics with Python
Data Scientist: Inference Specialist
Machine Learning Foundations

Hypothesis Testing with Python
Hypothesis Testing: Associations

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[blog1753350213]

I am reading the Introduction to Hypothesis Testing (Simulating a One-Sample T-Test) and am confused about something and was hoping this can be cleared up.

It says in Option 1:
“Alternative Hypothesis: The sample of 100 scores earned by Statistics Academy students came from a population with an average score that is greater than 29.92.
In this case, we want to know the probability of observing a sample average greater than or equal to 31.16 given that the null hypothesis is true. Visually, this is the proportion of the null distribution that is greater than or equal to 31.16 (shaded in red below). Here, the red region makes up about 3.1% of the total distribution. This proportion, which is usually written in decimal form (i.e., 0.031), is called a p-value.”

From my understanding, does this mean that there is only a 3.1% chance of a Statistics Academy student getting greater or equal to 31.16.

And then towards the end of the lesson it says:
“Impact of the Alternative Hypothesis
Note that different alternative hypotheses can lead to different conclusions. For example, the one-sided test described above (p = 0.031) would lead a data scientist to reject the null at a 0.05 significance level. Meanwhile, a two-sided test on the same data leads to a p-value of 0.062, which is greater than the 0.05 threshold. Thus, for the two-sided test, a data scientist could not reject the null hypothesis. This highlights the importance of choosing an alternative hypothesis ahead of time!”

Why would I reject the NULL hypothesis test if there was only a 3.1% chance of 100 Statistics Academy students getting a score greater than or equal to 31.16?