6.-Introduction-to-Hypothesis-Testing-and-Hypothesis-Testing-about-One-Population-Mean-z-Test

Introduction to Hypothesis Testing

  • Statistics and Probability overview.

Prayer/Reflection

  • Acknowledgment of the guidance of Almighty God and the Holy Spirit for strength and courage.

Hypothesis Concepts

Null Hypothesis (Ho)

  • Assumes no difference between two groups.

    • Example: Light color has no effect on plant growth.

Alternative Hypothesis (Ha)

  • Contradicts the null hypothesis, suggesting a potential effect or difference.

    • Example: Light color affects plant growth.

Definition of a Hypothesis

  • A hypothesis is an assertion about unknown parameters or properties concerning a population.

Hypothesis Testing

  • A process of generalizing population characteristics using sample statistics.

Steps in Hypothesis Testing

  1. Formulate null and alternative hypothesis.

  2. Specify the level of significance.

  3. Compute the test statistic or p-value.

  4. Determine the rejection region.

  5. Make a decision and conclusion regarding hypotheses.

Types of Tests

Non-Directional Test

  • Ex. Ho: μ = μ0

Directional Test

  • Ex. Ho: μ < μ0 or μ > μ0

Examples of Hypotheses

Example 1: COVID-19 Admissions

  • Ho: Average number of COVID-19 patients per week = 20.

  • Ha: Average number of patients ≠ 20.

Example 2: Average Grades

  • Ho: Average grade in Senior High STEM = 86.

  • Ha: Average grade > 86.

Example 3: Electric Company Consumption

  • Ho: Average consumption = 320kWh.

  • Ha: Average consumption < 320kWh.

Level of Significance (α)

  • Probability of rejecting the null hypothesis (Ho) when it is true.

  • Common values: 1%, 5%, 10%.

Decision Errors

Type I Error (α)

  • Incorrectly rejecting a true null hypothesis.

Type II Error (β)

  • Failing to reject a false null hypothesis.

Example: Court Trial Analogy

  • Hypothesis testing likened to a court trial.

    • Ho: Defendant is innocent.

    • Ha: Defendant is guilty.

Real-World Hypothesis Testing Examples

  1. COVID-19 Test Results:

    • Type I and Type II errors based on false test results.

  2. Cheating Scenario: Ann insisting she did not cheat despite observations of cheating.

  3. Self-Perception: Stephen denying being bald.

Test Statistics

  • Z-test: Used for normal population or large sample size (n >= 30).

  • T-test: Used for small sample sizes (n < 30) with unknown population standard deviation.

Example Scenario: Battery Lifespan Test

  • Ho: Average lifespan = 200 min, Ha: Average lifespan ≠ 200 min.

    • Critical value, significance, and rejection based on z-test.

Additional Hypothesis Testing Examples

  • Bottled Fruit Claim: Average capacity < 250 ml.

  • COVID-19 Life Span: Average lifespan > 70 years.

Practice Scenario

  • Automotive engineers testing a car's gas mileage against a company claim of 16 km/L. Try testing at a 5% level of significance.

Learning Targets

  • Illustrate hypotheses, significance levels, and rejection regions using z-Test.

  • Compute the correct test-statistic and draw conclusions based on results.

References

  • Ocampo & Tresvalles - "Probability, Statistics and Applications"