• A statistical method to test assumptions about a population parameter.
• The aim is to determine whether there is sufficient statistical evidence to support the hypothesis.
• Two main hypotheses:
  • Null hypothesis (\(H_0\)): No effect or no difference.
  • Alternative hypothesis (\(H_1\)): Effect or difference exists.
• Significance level (\(\alpha\)): Typically set to 0.05.

• Formulating hypotheses
• Choosing a test statistic based on data
• Collecting data
• Calculating P-value
• Compare the P-value
• Summarize the results and conclude

• A ggplot histogram to show distribution

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• Use of LaTex for formulas
• Test statistic for a one-sample z-test: \[ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \]
• P-value interpretation: \[ p = P(Z > |z| \,|\, H_0) \]

• A ggplot boxplot comparing two graphs

• A 3D visualisation of a test

• Recap key points.

• Importance of hypothesis testing in decision-making.

• Hypothesis testing provides a structured way to test assumptions.

• Visualization aids understanding and communication of results.

• Statistical tools like R make hypothesis testing accessible and reproducible.