• Objective: To understand the basic concepts of hypothesis testing.

• Null Hypothesis (H0): A statement of no effect or no difference.
• Alternative Hypothesis (Ha): A statement of an effect or difference.
• Test Statistic: A value used to make a decision in hypothesis testing.
• p-value: The probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true.

1. State the null and alternative hypotheses.
2. Collect and analyze data.
3. Calculate the test statistic.
4. Find the p-value.
5. Make a decision: reject or fail to reject the null hypothesis.

Suppose we want to test whether a new drug is more effective than an existing drug in reducing blood pressure.

• Null Hypothesis (H0): The new drug is equally effective as the existing drug.
• Alternative Hypothesis (Ha): The new drug is more effective than the existing drug.

• Let’s assume the test statistic follows a t-distribution.
• Calculate the test statistic using the sample data.

\[ t = \frac{{\text{Sample Mean} - \text{Population Mean}}}{{\text{Standard Error}}} \]

• After calculating the test statistic, find the p-value.
• The p-value represents the probability of observing the data if the null hypothesis is true.

\[ p\text{-value} = P(T > t) \]

• Compare the p-value to the significance level (α).
• If \(p\text{-value} < α\), reject the null hypothesis.
• If \(p\text{-value} ≥ α\), fail to reject the null hypothesis.

Let’s visualize the decision rule using a plot.