In our case, p-value is very low, meaning that there is strong evidence supporting that first basemen are taller.
> **Challenge**: Use the sample code in the notebook to test other hypothesis that: (1) First basemen and older that second basemen; (2) First basemen and taller than third basemen; (3) Shortstops are taller than second basemen
> 🚀 **Challenge**: Use the sample code in the notebook to test other hypothesis that: (1) First basemen and older that second basemen; (2) First basemen and taller than third basemen; (3) Shortstops are taller than second basemen
There are also different other types of hypothesis that we might want to test, for example:
* To prove that a given sample follows some distribution. In our case we have assumed that heights are normally distributed, but that needs formal statistical verification.
@ -222,8 +222,17 @@ In our case, the value 0.53 indicates that there is some correlation between wei
> More examples of correlation and covariance can be found in [accompanying notebook](notebook.ipynb).
## 🚀 Challenge
## Conclusion
In this section, we have learnt:
* basic statistical properties of data, such as mean, variance, mode and quartiles
* different distributions of random variables, including normal distribution
* how to find correlation between different properties
* how to use sound apparatus of math and statistics in order to prove some hypotheses,
* how to compute confidence intervals for random variable given data sample
While this is definitely not exhaustive list of topics that exist within probability and statistics, it should be enough to give you a good start into this course.
## Post-Lecture Quiz
@ -240,3 +249,4 @@ Probability and statistics is such a broad topic that it deserves its own course