Lecture Notes: Hypothesis Testing and Claims

Introduction

Objective: Conduct hypothesis testing by translating claims into symbols, identifying null and alternative hypotheses.

Claim: Mean temperature in summer is 82°.
- Phrase "is" indicates equality.
- Symbolic representation: X = 82 (X is the variable for mean temperature).
Complement: X ≠ 82 (since it could be either less or greater than 82).
Hypothesis Identification:
- Null Hypothesis (H₀): X = 82
- Alternative Hypothesis (Hₐ): X ≠ 82
- Use the equal sign to identify the null hypothesis.
Type of Test:
- Look at the alternative hypothesis symbol (≠).
- Conduct a two-tailed test (both directions: less than and greater than).

Claim: At most 3 accidents per month.
- "At most" implies less than or equal.
- Symbolic representation: X ≤ 3
Complement: X > 3
Hypothesis Identification:
- Null Hypothesis (H₀): X ≤ 3
- Alternative Hypothesis (Hₐ): X > 3
- The equal bar in X ≤ 3 indicates it as the null hypothesis.
Type of Test:
- Use the symbol in the alternative hypothesis (X > 3).
- Conduct a right-tailed test (pointing to the right).

Claim: More than 62%
- "More than" suggests greater than.
- Convert percentage to decimal for calculations: X > 0.62
Complement: X ≤ 0.62 (not greater implies could be less or equal).
Hypothesis Identification:
- Null Hypothesis (H₀): X ≤ 0.62
- Alternative Hypothesis (Hₐ): X > 0.62
- The equal bar in X ≤ 0.62 indicates it as the null hypothesis.
Type of Test:
- Look at the symbol in the alternative hypothesis (X > 0.62).
- Conduct a right-tailed test (arrow points to the right).

Always identify the null and alternative hypotheses based on the presence of the equal sign.
Determine the type of test (left-tailed, right-tailed, two-tailed) by examining only the alternative hypothesis.
Claims may not always be the null hypothesis; they depend on the symbol used.