• Hypothesis testing is a statistical method used to make inferences or decisions about population parameters based on sample data.
• It is a key concept in inferential statistics used across various fields.

• Null Hypothesis (\(H_0\)): There is no effect or no difference.

  \[ H_0: \mu = \mu_0 \]

• Alternative Hypothesis (\(H_A\)): There is an effect or a difference.

  \[ H_A: \mu \neq \mu_0 \]

1. Formulate the hypotheses.
2. Choose the significance level (commonly \(\alpha = 0.05\)).
3. Collect data and compute the test statistic.
4. Make a decision by comparing the p-value with \(\alpha\).
5. Draw conclusions.

Example: - Test whether the mean height of students in a school differs from 170 cm.

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• Hypothesis testing is a critical tool in statistics.
• It helps determine whether to reject or fail to reject the null hypothesis.
• Visualizations like p-value plots and boxplots help in understanding the data and making informed decisions.

• Z-test statistic formula:

\[ Z = \frac{\bar{X} - \mu_0}{\frac{\sigma}{\sqrt{n}}} \]

• t-test statistic formula:

\[ t = \frac{\bar{X} - \mu_0}{\frac{s}{\sqrt{n}}} \]

Both help in hypothesis testing for population means.