Download Stats Final Exam Study Guide: Hypothesis Testing, Bayes' Theorem, Genetics - Prof. Yulia D and more Exams Mathematics in PDF only on Docsity! STUDY GUIDE for FINAL EXAM Chapters 1 (Section 1.7.3), 2, 3, 4, and 5 Making Inferences 1. Describe Type I and Type II errors in Hypothesis Testing. Why we would never accept the null hypothesis? 2. The hourly wages in a particular industry are normally distributed with mean $13.20 and standard deviation $2.50. A company in this industry employs 40 workers, paying them an average of $12.20 per hour. Can this company be accused of paying substandard wages? Use an a = 0.01 level test. 3. People at risk of sudden cardiac death can be identified using the change in a signal averaged electrocardiogram before and after prescribed activities. The current method is about 80% accurate. The method was modified, hoping to improve its accuracy. The new method is tested in 50 people and gave correct results on 46 patients. Is this convincing evidence that the new method is more accurate? Use a 0.04 level of significance. 4. Does the observation of 25 heads in 35 tossing of a coin support the hypothesis that the coin is balanced? 5. The numbers of first births to 700 women are shown by month from the University Hospital of Basel, Switzerland. Month Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec Births 66 63 64 48 64 74 70 59 54 51 45 42 State the hypothesis to test that births are spread uniformly through the year. Use a 0.05 level of significance. 6. A study was done to investigate the association between the age at which breast cancer was diagnosed and the frequency of breast self-examination. The following table classifies the women in the sample according to these two criteria. Frequency of Breast Self-examination Age at Diagnosis of Breast Cancer Monthly Occasionally Never < 45 91 90 51 45 – 59 150 200 155 60 + 109 198 172 Test the hypothesis that the frequency of sex-examination is related to the age of breast cancer diagnosis. Use a 0.01 level of significance. Transfer Evidence 1. Define each of the following probabilities: a) Pr (E | HP, I) b) Pr (E | HD, I) c) Pr (HP | E, I) d) Pr (HP | I) Which of these probabilities should be addressed by a scientist and which by a jury? 2. State the odds form of Bayes’ Theorem for the single crime stain evidence. Use appropriate notations. 3. Formulate the three principles of evidence interpretation. 4. Explain why )|Pr(),|Pr(),|Pr( IGIHGIHG SDSPS == . 5. Give an example of a Transpose Conditional Fallacy. 6. What is wrong with the following statement: “This crime occurred in a city of 80,000 people. This blood type would be found n approximately 8,000 people. The evidence has provided a probability of 1 in 8,000 that the defendant is guilty and thus has no relevance. ” Population Genetics 1. Find the proportions of the three alleles from the following set of genotypic proportions: A1A1 A1A2 A1A3 A2A2 A2A3 A3A3 0.24 0.24 0.22 0.14 0.08 0.08 2. Assuming Hardy-Weinberg Equilibrium, find the expected genotypic proportions in the previous example. 3. Describe possible conditions disturbing Hardy-Weinberg Equilibrium. 4. For a given pedigree, compute the inbreeding coefficient of X. 5. Find the probability with which non-inbred half-sibs both have A1A2 genotypes if they belong to a population in Hardy-Weinberg Equilibrium with proportions p1 = 0.37 and p2 = 0. 06 for alleles A1 and A2. 6. Describe a phenomenon of the genetic drift (inbreeding in population).
