Testing hypothesis about the mean of normal population when sigma known examples

Testing a hypothesis involves a structured process to determine whether a specific claim or assumption about a population is true. It typically starts with forming two hypotheses: the null hypothesis (H₀), which assumes no effect or no difference, and the alternative hypothesis (H₁), which represents the claim being tested.
Formulate Hypotheses: Define H₀ and H₁ based on the research question.
Select Significance Level (α): Choose a probability threshold (commonly 0.05) for rejecting H₀.
Collect Data: Gather relevant sample data.
Conduct Statistical Test: Apply a test (e.g., t-test, chi-square) to the data.
Calculate Test Statistic: Compute a value (z, t, etc.) to assess the hypotheses.
Determine p-value: Measure the probability of observing the data under H₀.
Compare p-value and α: If the p-value ≤ α, reject H₀.
Draw Conclusion: Decide whether the evidence supports H₁.
Interpret Results: Consider practical significance along with statistical outcomes.
Report Findings: Share the conclusion in context of the original claim.

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