vault backup: 2025-01-15 20:31:27

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Statistics and Probability/Mock exam run 1.md

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+
+### Null hyposthesis
+
+### Confidence interval
+Interval which is expected to contain the parameter
+$$
+CI = \bar{x} \pm z \frac{s}{\sqrt{n}}
+$$
+Where $z\frac{s}{\sqrt{n}}$ is the variation in our estimate.
+
+
+### T-Test
+Used to determine if there is a significant difference between the means of two groups.
+
+We have to assume:
+- Data follows a normal distribution
+- each observation is independent
+
+$$
+t = \frac{\text{mean} - \text{theoretical value}}{s\sqrt{n}}
+$$