Chapter 8 - Hypothesis Testing (1)1

Chapter 8 - Hypothesis Testing

8.1 Basics of Hypothesis Testing Definitions

• Hypothesis Testing is a statistical method used to make inferences about population parameters based on sample data.

• Involves two hypotheses: Null Hypothesis (H0) and Alternative Hypothesis (H1).

8.1 Basics of Hypothesis Testing Acronym - H A T N C

• H: Hypotheses - Formulating H0 and H1 based on research questions.

• A: Alpha (α) - Significance level, probability of rejecting the null hypothesis when it is true.

• T: Test Statistic - A standardized value that is calculated from sample data.

• N: Null Distribution - Theoretical distribution of the test statistic under the null hypothesis.

• C: Conclusion - Drawing a conclusion based on the comparison of the test statistic to critical values.

8.1 Basics of Hypothesis Testing Hypotheses

• Null Hypothesis (H0): Statement of no effect or no difference.

• Alternative Hypothesis (H1): Statement indicating the presence of an effect or difference.

8.1 Basics of Hypothesis Testing Hypotheses Types

• Two-tailed test: Sign used in H1: ≠ (not equal) - Tests for effects in both directions.

• Left-tailed test: Sign used in H1: < (less than) - Tests if the population parameter is significantly less than a certain value.

• Right-tailed test: Sign used in H1: > (greater than) - Tests if the population parameter is significantly greater than a certain value.

8.1 Basics of Hypothesis Testing Assumptions

• Data should be drawn from a random sample.

• The sample size must be adequate to assume normality (n > 30 or np & n(1-p) > 5).

• The population should be normally distributed if the sample size is small (n < 30).

8.1 Basics of Hypothesis Testing Test

• Steps to conduct a hypothesis test include:

  • Define hypotheses (H0, H1).

  • Choose significance level (α).

  • Calculate test statistic.

  • Determine critical value or p-value.

  • Make a decision: reject or fail to reject H0.

8.1 Basics of Hypothesis Testing Numbers

• Significance Level (α) examples: 0.01, 0.05, 0.10.

• P-value: Probability of obtaining the observed results given that H0 is true.

8.1 Basics of Hypothesis Testing Conclusion

• Depend on p-value and α level, if p-value < α reject H0.

• If p-value > α, fail to reject H0.

8.1 Basics of Hypothesis Testing Errors

• Type I Error (α): Incorrectly rejecting the null hypothesis when it is true.

• Type II Error (β): Failing to reject the null hypothesis when it is false.

8.1 Basics of Hypothesis Testing Example

• Captain Ben's passenger jets:

  • a) Type I error: Declaring the flight safe when it isn’t (false security). Type II error: Declaring the flight unsafe when it is safe (false alarm).

  • b) Consequences: Type I error risks safety; Type II error could lead to financial loss through cancellations. Type I is often more critical in safety-related decisions.

  • c) Choosing a significance level: α = 0.05 is commonly accepted, balancing between Type I and II errors.

8.1 Basics of Hypothesis Testing Power of the Test

• Power: Probability of correctly rejecting a false null hypothesis (1 - β).

• Influenced by sample size, significance level, and effect size.

8.2 Testing for 1 Proportion H A T N C

• Importance of defining hypotheses and correctly interpreting data for proportion testing.

8.2 Testing for 1 Proportion Example

• Study with 926 Internet users on two-factor authentication usage.

  • Null hypothesis: H0: p ≤ 0.5 (50% or less)

  • Alternative hypothesis: H1: p > 0.5 (more than 50%)

8.2 Testing for 1 Proportion Example #2

• Sleepwalking study findings: 29.2% of adults have sleepwalked.

  • Testing claim: H0: p ≥ 0.30; H1: p < 0.30 using α = 0.05.