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# Stat 1

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### Stat 1

1. 1. Example : “ The mean of all bags of pretzels differs fromthe advertised weight of 454 grams.”Null : “ The mean of all bags of pretzels equals theadvertised weight of 454 grams.” H0:µ = 454 gramsAlternative : “ The mean of all bags of pretzels differs fromthe advertised weight of 454 grams.” H1:µ ≠ 454 grams
2. 2. Hypothesis Testing – a method used to make decisions or judgment.Steps in Hypothesis Testing1. Formulate the Null Hypothesis2. Formulate the Alternative Hypothesis3. Specify the Level of Significance4. Determine the Critical Value5. Compute for the test of Statistics6. Decision or Conclusion
3. 3. • Type I and Type II errors Our Decision Truth of H0 If we accept H0. If we reject H0. If H0 is true Correct decision; Type I error no error If H0 is false Type II error Correct decision; no error• Conclude a test using the P-value and Level of Significance α. If P-value ≤ α, we reject the null hypothesis and say thedata are statistically significant at the level α. If P-value > α, we do not reject the null hypothesis.
4. 4. SAMPLE PROBLEMA. A certain task can be done at an average of 40 mins.w/ standard deviation of 8. A group of 16 workers, given w/trainings, found the average is only 35 mins. Test thehypothesis w/ 0.01 level.
5. 5. Statistical Test Formulas…B. Test for a single mean when variance is unknown & sample is more than 30.
6. 6. SAMPLE PROBLEMB. Under the old system, it took an average of 50 minutes/student toregister. If a random sample of 35 students had an average of 42 minutes toregister w/ standard deviation of 11.9 under the use of modern machines.Test the hypothesis under 0.01 level.
7. 7. Statistical Test Formulas…C. Test for a single mean when variance is unknown & sample is not more than 30.
8. 8. SAMPLE PROBLEMC. In a certain test given under the supervised condition, the meanscore of 25 students is 62 w/ standard deviation of 10. A student who tookunder the NS condition turned in mean score of 87 . Test the hypothesisunder 0.01 level.
9. 9. Statistical Test Formulas…D. Test for the mean of paired observations
10. 10. SAMPLE PROBLEMD. A team of heart surgeons knows that many patients who undergo corrective heart surgery have a dangerous buildup of anxiety before their scheduled operations. The staff psychiatrist at the hospital has started a new counseling program intended to reduce this anxiety. From the given data, can we conclude that the counseling sessions reduce anxiety? Use 0.01 level of significance. B A d=B–A Patients Score Score After Difference Before Counseling Counseling Jan 121 76 45 Tom 93 93 0 Dianne 105 64 41 Barbara 115 117 -2 Mike 130 82 48 Bill 98 80 18 Frank 142 79 63 Carol 118 67 51 Alice 125 89 36
11. 11. Statistical Test Formulas…E. Test for the difference of the means from independent samples when variance isknown.
12. 12. SAMPLE PROBLEME. A class of 40 students is taught by method “A” and A class of 36is taught by method “B”. Both are given same test . The mean scores are 78and 74 respectively. At standard deviation of 5 & 0.05 level, Test thehypothesis.
13. 13. Statistical Test Formulas…F. Test for the difference of the means from independent samples when variance isunknown and samples are more than 30.
14. 14. SAMPLE PROBLEM F. The average grade of 50 senior students in Math is 85 w/ s=10.2, while a group of 60 senior students got 82 w/ s=8.9. Can the difference in the mean be attributed to chance using 0.05 level.
15. 15. Statistical Test Formulas…G. Test for the difference of the means from independent samples when variance isunknown and samples are not more than 30.
16. 16. SAMPLE PROBLEMG. At the beginning of SY, the mean score of 24 students in anachievement test was 45 w/ s=6. At the end of SY, the mean score of thesame test was 50 w/ s=5. Find if the class has improved. Use 0.05 level ofsignificance.
17. 17. Statistical Test Formulas…H. Test about single proportion.
18. 18. SAMPLE PROBLEMH. In DLSU, it is estimated that 25% of students have cars oncampus. Does this seem to be valid estimate if random sample of 90students, 28 are found to have cars? Use alpha 0.05.
19. 19. Statistical Test Formulas…I. Test of comparing two proportions
20. 20. SAMPLE PROBLEM I. In cheating matters among students, 144 or 41.4 % of 348 from homes of good socio-eco status were found to have cheated in some test. While 133 or 50.2 % of 265 students of poor socio-eco status also cheated on same test. Is there a true difference in the incidence of cheating in these 2 groups? Use alpha 0.10
21. 21. Statistical Test Formulas…J. Test on single variance or standard deviation.
22. 22. SAMPLE PROBLEMJ. The life of a certain batteries are approximately distributed w/standard deviation equal to 0.09 yr. If random sample of 10 of these haves=1.2 years. Is s> 0.9 year? Use alpha 0.05
23. 23. Statistical Test Formulas…K. Test on two variances or standard deviations
24. 24. SAMPLE PROBLEMK. A group of Mass Com students found that 17 incoming calls lastan average of 5.16 minutes w/ variance of 2.12 & 12 outgoings’ last anaverage of 4.13 minutes w/ variance of 1.36. Test the Hypothesis thatvariances are equal. Use alpha 0.05.