lesson one (Q4) ppt -.pptx in statistic and probability

Senior high

1. Here is where your presentation begins Math Subject for High School Probability and Statistics

2. Illustrates: a. null hypothesis, b. alternative hypothesis, c. level of significance, d. rejection region; e. types of errors in hypothesis testing;

3. Definition of Terms 3 NULL HYPOTHESIS denoted by (Ho)- a statement that there is no difference between a parameter and a specific value, or that there is no difference between two parameters. ALTERNATIVE HYPOTHESIS denoted by (H1)- a statement is the opposite or negation of the null hypothesis LEVEL OF SIGNIFICANCE denoted by alpha or refers to the degree of significance in which we accept or reject the null hypothesis.  

4. Definition of Terms 4 TWO-TAILED TEST vs ONE-TAILED TEST When the alternative hypothesis is two- sided like Ha: μ ≠ μ0, it is called two- tailed test .   When the given statistics hypothesis assumes a less than or greater than value, it is called one-tailed test   REJECTION REGION also known as critical region is the set of all values of the test statistics that causes us to reject the null hypothesis.  

5. TYPE I ERROR -t his is typically set by the researcher before conducting the test (e.g., 0.05). It represents the threshold for rejecting the null hypothesis 5   TYPES OF ERROR TYPE II ERROR -determine the critical value for the test based -use statistical tables or software to find the probability of failing to reject the null hypothesis given true effect size.

6. Hypothesis Testing It is a decision-making procs for evaluating claims about a population Hypothesis is an assumption of conjecture about a population parameter which may or may not be true Example: Does the mean height of grade 11 student differ from .66 inches? 6

7. 7 7 NULL HYPOTHESIS ALTERNATIVE HYPOTHESIS it is denoted by Ho. It is initial claim It shows no significant difference, no changes, nothing happened, no relationship between two parameter. The independent variables has no effect on the dependent variable. It is denoted by Ha or H1 It is contrary to the null hypothesis. It shows that there is significant difference, an effect, change, relation ship between a parameter and specific value.

8. 8 8 NULL HYPOTHESIS ALTERNATIVE HYPOTHESIS = Equal to the same as, not changed from, is Not equal, different from, changed from, not the same as > greater than, above, higher than, longer than, bigger than, increased, at least <less than, below lower than, smaller than, shorter than, decreased or reduced from, at most NULL HYPOTHESIS ALTERNATIVE HYPOTHESIS = Equal to the same as, not changed from, is

9. 9 9 Example in illustrating null and alternative hypotheses. State the null and alternative hypothesis for each statement. The school record claims that the mean score in Math of the incoming Grade 11 students is 81. The teacher wishes to find out if the claim is true. She tests if there is significant difference between the batch mean score and the mean score of students in her class .

10. Ho: the mean score of the incoming grade 11 students is 81 10 Null and alternative Hypothesis in words Null and alternative Hypothesis in symbol         Ha: the mean score of the incoming grade 11 students is not 81 Ho: μ =81 Ho: μ 81  

11. Identify whether null hypothesis or alternative hypothesis. 1.The average age of bus drivers in Metro Manila is 38.8 years 2.The average number of calories of a low- calorie meal is at most 300. 11

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13. Level of Significance 13 Significance is defined as the quality of being statistically significant Level of significance It is denoted by alpha refers to the degree of significance in which we accept or reject the null hypothesis.  

14. 14 In symbol, it is written as: = 0.01 = 0.05 or = 0.10 if the alternative hypothesis used then alpha will be divided by 2 /2 = 0.005 = 0.025 or /2 = 0.05   Example 1. Maria uses 5% level of significance in proving that there is no significant change in the average number of enrollees in the 10 section for the last two years.

15. 15 In symbol, it is written as: = 0.01 = 0.05 or = 0.10 if the alternative hypothesis used then alpha will be divided by 2 /2 = 0.005 = 0.025 or /2 = 0.05   Determine the value of or /2 based on the alternative hypothesis in decimal form Example 2: In 2025, it was recorded that around 34% of the population in 2015 were not married. The researcher surveyed a random sample of 500 couples. He found that 18% of them were living together but unmarried. Test at the 5% significance level if the current percentage of unmarried couples is different from 34  

16. 16 16 TWO- TAILED TEST VS ONE-TAILED TEST When the alternative hypothesis is two-sided like it is called two-tailed test. When the given statistics hypothesis assumes a less than or greater then value, it is called one-tailed test not equal, different from, changed from, not the same > Greater than, above, lower than, smaller than, shorter than, decreased or reduced from < less than, below, lower than, smaller than, shorter than, decreased or reduce from. = equal to, the same as, not change from, is  

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19. 19 19 Determine if one-tailed test or to tailed test fits the given alternative hypothesis. The mean height of grade 12 student is less than 66 inches. The standard deviation of their height is not equal to 5 inches. Male Grade 7 and grade 12 students differ in height on average. The portion of senior male student’s height is significantly higher than that of senior female student. the average grade of grade 11 students in statistic is lower than their average grade in calculus

20. 20 ILLUSTRATION OF THE REJECTION REGION Rejection region, also known as critical region is the set of all values of the test statistical that causes us to reject the null hypothesis The non-rejection Region B (or acceptance region) is the set of all values of the test statistic that causes to fail to reject the null hypothesis The critical value is a point (boundary) on the test distribution that is compared to the test statistic to determine if the null hypothesis would be rejected

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