Overview
This lecture focuses on how to properly write conclusions for hypothesis tests by relating p-values, claims, and evidence to the null and alternative hypotheses.
Writing Hypothesis Test Conclusions
- Conclusions should address the claim and present supporting evidence, not just state "reject" or "fail to reject" the null hypothesis.
- A proper conclusion links test results back to the specific claim in question.
Interpreting the P-value
- If the p-value ≤ significance level (α), the data is unlikely due to sampling variability; reject the null hypothesis.
- A low p-value with unbiased data is considered evidence against the null hypothesis and supports the alternative hypothesis.
- If the p-value > significance level, fail to reject the null hypothesis; no significant evidence against the null.
Claims and Evidence Types
- Claims can be about the null hypothesis (H₀) or the alternative hypothesis (H₁ or Ha).
- Four possible conclusion scenarios:
- Claim = H₀ & low p-value: Evidence to reject the claim.
- Claim = H₀ & high p-value: No significant evidence to reject the claim.
- Claim = Ha & low p-value: Evidence to support the claim.
- Claim = Ha & high p-value: No significant evidence to support the claim.
Importance of Good Data
- Conclusions are only valid if data is unbiased and assumptions are met; bad data invalidates p-value interpretations.
Example: Mean Body Temperature
- Null hypothesis (H₀): mean body temperature = 98.6°F.
- Alternative hypothesis (Ha): mean < 98.6°F (the claim).
- Identify whether the claim matches H₀ or Ha before writing your conclusion.
Key Terms & Definitions
- Null Hypothesis (H₀) — baseline statement of "no effect" or "no difference"; may include "equal to".
- Alternative Hypothesis (Ha) — statement indicating a change, effect, or difference; usually ≠, >, or <.
- P-value — probability of observing data as extreme as the sample, assuming H₀ is true.
- Significance Level (α) — threshold for rejecting H₀; commonly set at 0.05.
- Reject the null hypothesis — conclude there is significant evidence against H₀.
- Fail to reject the null hypothesis — conclude there is not enough evidence against H₀.
Action Items / Next Steps
- Practice identifying the claim in hypothesis test problems and writing full, evidence-based conclusions.
- Review notes on unbiased sampling and test assumptions as these impact the validity of conclusions.