Introduction to Hypothesis Testing

Key Concepts

• Null Hypothesis (H₀): The status quo or current accepted value that is believed to be true.
• Alternative Hypothesis (H₁ or Hₐ): The contradictory claim to the null hypothesis; what the researcher is trying to prove.

Example 1: Company XYZ Calculators

• Claim: Average mass of calculators is 450 grams.
• Null Hypothesis (H₀): µ = 450 grams (the average mass is 450 grams).
• Alternative Hypothesis (H₁): µ ≠ 450 grams (the average mass is different from 450 grams).

Example 2: School Graduation Rates

• Claim: At least 80% of students will complete high school.
• Null Hypothesis (H₀): p ≥ 0.80 (the proportion of students completing high school is at least 80%).
• Alternative Hypothesis (H₁): p < 0.80 (the proportion of students completing high school is less than 80%).

Example 3: High School GPA

• Claim: Average GPA of students is different from 2.7.
• Null Hypothesis (H₀): µ = 2.7 (the average GPA is 2.7).
• Alternative Hypothesis (H₁): µ ≠ 2.7 (the average GPA is different from 2.7).

Example 4: Vehicle Ownership in Town XYZ

• Claim: Percentage of residents who own a vehicle is no more than 75%.
• Null Hypothesis (H₀): p ≤ 0.75 (the proportion of residents owning a vehicle is no more than 75%).
• Alternative Hypothesis (H₁): p > 0.75 (the proportion of residents owning a vehicle is greater than 75%).

Conclusion

• Understanding how to state the null and alternative hypotheses is critical in hypothesis testing.
• The null hypothesis is considered correct until evidence suggests otherwise.