Lecture Notes: Hypothesis Testing Decisions and Conclusions

Key Definitions

• Null Hypothesis (H₀):
  • The baseline statement against which we test.
• Alternative Hypothesis (Hₐ):
  • The claim we are trying to support with evidence.

Decision Language

• Decisions:
  • We either "reject" or "do not reject" the null hypothesis.
  • Important: Never use the word "accept" for the null hypothesis.
• Error Consideration:
  • Errors can occur in decision-making which explains the avoidance of the term "accept."
• Conclusion Wording:
  • Based on evidence, the decision must be clearly articulated.

Writing Conclusions

• If Reject Null (H₀):
  • "There is sufficient evidence to support the alternative claim."
  • Specify the claim's context rather than using just notation.
• If Do Not Reject Null (H₀):
  • "There is not sufficient evidence to support the alternative claim."
  • Again, specify the claim context.

Example 1: Applesauce Manufacturer

• Context: FDA labeling issue, a claim of less content than labeled.
• Hypotheses:
  • Null (H₀): Mean (µ) = 64 ounces (as per label)
  • Alternative (Hₐ): Mean (µ) < 64 ounces (shorting customers)
• Decision: Reject the null hypothesis.
• Conclusion:
  • "There is sufficient evidence to support the claim that the manufacturer of applesauce is shorting customers."

Example 2: Massage Therapist Technique

• Context: Reducing migraines via a new technique.
• Hypotheses:
  • Null (H₀): Proportion (p) = 0.152 (15.2% of Americans with migraines)
  • Alternative (Hₐ): Proportion (p) < 0.152 (technique decreases frequency)
• Decision: Do not reject the null hypothesis.
• Conclusion:
  • "There is not sufficient evidence to support the claim that the massage therapist's technique reduces the frequency and intensity of migraines."

Additional Notes

• Focus on Null Hypothesis for Decision Making:
  • Decisions are framed around the null hypothesis.
  • Conclusions are framed around the support or lack of support for the alternative hypothesis.
• Wording:
  • Language contextualization is important for clarity in conclusions.