HYPOTHESIS TESTING - STATISTICS AND PROBABILITY

sTATISTICS

1. Statistics - MA-MATH801 Prepared by: Mr. John Luis M. Bantolino

2. Table of contents 01 04 02 05 03 06 Hypothesis Testing Types of Hypothesis Errors of Probability in Hypothesis Testing Regions of Rejection Level of Significance Tabular Value

3. Hypothesis Testing 01

4. Introduction Hypothesis testing is a fundamental concept in statistics that helps researchers and scientists make informed decisions about population parameters based on sample data. This lesson will cover various aspects of hypothesis testing, including types of hypotheses, errors of probability, regions of rejection, level of significance, and tabular values in hypothesis testing.

5. Types of Hypothesis 02

6. Opposes the null hypothesis. Represents what the researcher is trying to prove. Denoted as or   Represents a default assumption. Typically states that there is no effect, no difference, or no change. Denoted as   Null Hypothesis: Alternative Hypothesis:

7. Errors of Probability in Hypothesis Testing 03

8. T y pes of Errors is TRUE is FALSE DECISION REJECT Type I error Correct Decision FAILED TO REJECT Correct Decision Type II error DECISION Type I error Correct Decision Correct Decision Type II error a. Type I Error (False Positive): Incorrectly rejecting a true null hypothesis. b. Type II Error (False Negative): Incorrectly failing to reject a false null hypothesis.

9. Regions of Rejection 04

10. Critical Region: The range of values for which the null hypothesis will be rejected. Determined by the level of significance (α) and the distribution of the test statistic. Non-Critical Region: The range of values for which the null hypothesis will not be rejected.

11. Level of Significance 05

12. The level of significance refers to the degree of significance in which we reject and fail to reject the null hypothesis. In hypothesis testing, 100 % accuracy does not guarantee in rejecting and in failing to reject a null hypothesis. The generally accepted levels are 1%, 5% and 10 %. However, the 5% level of significance has become the most common in practice.

13. Tabular Value 06

14. The tabular value (critical value) is obtained from statistical tables and helps determine the cutoff point for rejecting the null hypothesis.