When I was a student, I learned the concept of the p-value. But I didn’t quite understand what is that.
In the course material, it said “The p-value is the smallest level of significance at which H0 would be rejected when a specified test procedure is used on a given data set. Once the p-value has been determined, the conclusion at any particular level alpha results from comparing the p-value to alpha.”
I know it’s hard to understand what it’s talking about. No worries! Because I’m confused also.
After rethinking this, the main point is: what is the possibility you’ll be wrong according to the information(data) you have. Usually, the p-value is 0.05, so you’ll be wrong with the 0.05 possibility.
Use an interactive chart to explain this. (For a better experience, please use a desktop or horizontal smartphone)
So, One case is when the p-value is smaller, the average gap between sample data and mu0 need to be bigger to have the confidence to reject H0.
Free free to play the interactive chart to feel the different situations.
The t-table data is from https://home.ubalt.edu/ntsbarsh/business-stat/StatistialTables.pdf
The normal distribution calculation formula is from https://en.wikipedia.org/wiki/Normal_distribution