Statistic and Probability. G11 STEM.pptx

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1. TESTING HYPHOTHESIS Reporter 1 Reporter 2 Reporter 3 Reporter 4 Reporter 5 STATISTICS AND PROBABILITY STEM Quarter 4

2. 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 a significant difference between the batch mean score and the mean score of students in her class. Reporter 1 Reporter 2 Reporter 3 Reporter 4 Reporter 5 𝐻𝑜: The mean score of the incoming Grade 11 students is 81 or 𝜇 = 81. 𝐻𝑎: The mean score of the incoming Grade 11 students is not 81 or 𝜇 ≠ 81. 𝐻𝑜: The mean score of the incoming Grade 11 students has no significant difference with the mean score of her students or 𝜇 = 𝑥̅. 𝐻𝑎: The mean score of the incoming Grade 11 students has a significant difference with the mean score of her students or 𝜇 ≠ 𝑥̅.

3. A social worker wants to test (at ꭤ = 0.05) whether the average body mass index (BMI) of the pupils under feeding program is different from 8.2 kg. Null and Alternative Hypothesis in words 𝐻𝑜: 𝐻𝑎: Null and Alternative Hypothesis in symbol 𝐻𝑜: 𝐻𝑎: The average BMI of the pupils under feeding program is different from 18.2 The average BMI of the pupils under feeding program is not different from 18.2 𝜇 = 18.2 𝜇 ≠ 18.2

4. A DTI representative wants to test at 99% confidence level whether the average content of Soda X is less than 330 ml as indicated in the label. Null and Alternative Hypothesis in words 𝐻𝑜: 𝐻𝑎: Null and Alternative Hypothesis in symbol 𝐻𝑜: 𝐻𝑎: 𝜇 < 330 𝜇 ≥ 330 The average content of soda X is less than 330 ml. The average content of soda X is greater than or equal to 330 ml.

5. In 2015, it was recorded that around 34% of the population in 2015 were not married. A researcher surveyed a random sample of 500 couples. He found out that 18% of them were living together but unmarried. Test at 5% significance level if the current percentage of unmarried couples is different from 34%. Null and Alternative Hypothesis in words 𝐻𝑜: 𝐻𝑎: Null and Alternative Hypothesis in symbol 𝐻𝑜: 𝐻𝑎: 𝜇 ≠ 34% 𝜇 = 34% The current percentage of unmarried couples is different from 34%. The current percentage of unmarried couples is 34%.

6. LEVEL OF SIGNIFICANCE ✓ The level of significance denoted by alpha or 𝛂 refers to the degree of significance in which we accept or reject the null hypothesis. ✓ 100% accuracy is not possible in accepting or rejecting a hypothesis. ✓ The significance level α is also the probability of making the wrong decision when the null hypothesis is true. MOST COMMON LEVEL OF SIGNIFICANCE 𝛂 = 1% = 0.01 𝛂 = 5% = 0.05 𝛂 = 10% = 0.10 Example: 𝐻𝑜: 𝐻𝑎: 𝜇 = 20 𝜇 ≠ 20 There is a 5% chance of concluding that 𝜇 ≠ 20 when in fact 𝜇 = 20 𝛂 = 5% = 0.05

7. Rejecting the null hypothesis when it is in fact true. TYPE I ERROR TYPE II ERROR 𝛂 = probability of type I error 𝛂 = P (rejecting 𝐻𝑜 | 𝐻𝑜 is true Criminal trial in a court Type I occurs when the judge convicts an innocent person Fail to reject the null hypothesis when it is in fact false. ß = probability of type II error ß = P ( fail to reject 𝐻𝑜 | 𝐻𝑜 is false Criminal trial in a court Type II occurs when the judge acquitted a guilty defendant

8. Reporter 1 Reporter 2 Reporter 3 Reporter 4 Reporter 5 The null hypothesis is Decision True False Reject 𝐻𝑜 Type I error ( 𝛂 ) Correct Decision Fail to reject 𝐻𝑜 Correct Decision Type II error ( ß ) The defendant is DECISION TRUE FALSE The judge finds the defendant guilty Type I error ( 𝛂 ) Correct Decision The judge finds the defendant innocent Correct Decision Type II error ( ß )

9. Reporter 1 Reporter 2 Reporter 3 Reporter 4 Reporter 5 Analyze the following conclusions. Identity if a Type I Error , Type II Error , or a Correct Decision was committed. You are making a conclusion on your research; you find out that your null Hypothesis is… True and you reject it ___________________ True and you fail to reject it ______________ False and you reject it ______________ False and you fail to reject it ___________ Type I Error Correct Decision Type II Error Correct Decision

10. Reporter 1 Reporter 2 Reporter 3 Reporter 4 Reporter 5

11. Two-Tailed Test vs One-Tailed Test Reporter 1 Reporter 2 Reporter 3 Reporter 4 Reporter 5 ✓ 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 . ≠ not equal, different from, changed from, not the same as > greater than, above, higher than, longer than, bigger than, increased < less than, below, lower than, smaller than, shorter than, decreased or reduced from = equal to, the same as, not changed from, and is

12. MEMBERS Reporter 1 Reporter 2 Reporter 3 Reporter 4 Reporter 5

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