The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STAT 155 Introductory Statistics Review for the Final Exam Fall 2006 12 05 06 Review for the Final Exam 1 Final Exam Format Closed book closed notes One formula sheet double sided Calculator Scantron and 2 pencils Tables will be provided 50 multiple choice questions at least a half based on materials covered after the 2nd midterm 12 05 06 Review for the Final Exam 2 Suggestions for your review Read the lecture notes carefully Go over Homework problems practice midterms and midterms Solve the problems yourself Do the practice problems in this final review 12 05 06 Review for the Final Exam 3 Office hours Monday 12 11 Wednesday 12 13 11 am 1 pm Solutions to Hwk 22 available at Blackboard from Thursday 12 7 12 05 06 Review for the Final Exam 4 What have we learned in STAT 155 Basic data analysis techniques Simple linear regression Elementary probability Sampling distributions Point estimation confidence intervals Hypothesis testing Z test 12 05 06 Review for the Final Exam 5 Review of Chapter 1 Visualization tools stem and leaf histogram bar graph pie chart boxplot time plot Measures of Location mean median mode Measures of Variability range interquartile range standard deviation variance The five number summary Effect of linear transformation Normal distribution Standardization normal distribution calculation 12 05 06 Review for the Final Exam 6 Review of Chapter 2 Scatterplots interpretation Correlation definition and properties Least Squares Regression Find the regression equation prediction and interpretation the meaning of r2 Regression diagnostics Residuals outliers influential observations lurking variables 12 05 06 Review for the Final Exam 7 Review of Chapter 4 Sample spaces events union intersection complement disjoint events tree diagram Venn diagram Axioms and properties of probability Addition rule P A B P A P B P A B Conditional probability P A B P A B P B Multiplication rule P A B P A B P B P B A P A Independence P A B P A P B Bayes rule no need to memorize derive it Rules for expected values variances 12 05 06 Review for the Final Exam 8 Review of Chapter 5 Binomial distribution Sampling distribution for counts and proportions Table C mean standard deviation Normal approximation continuity correction Sampling distribution of X 1 X X X2 X2 n 2 i If X is normal X is normal ii If X is nonnormal X is approximately normally distributed for sufficiently large sample size 12 05 06 Review for the Final Exam 9 Road map for CI and HT Lectures 18 22 1 sample or two samples 1 sample or p 2 samples 1 2 or p1 p2 CI or HT For p1 p2 use SED or SEDp Ha 1 sided or 2 sided Which P value to calculate Decision reject or accept H0 CI what is the margin of error HT which 4 steps Relationship between CI and HT 12 05 06 Review for the Final Exam 10 Practice Problem 1 A fair coin is tossed 200 times what is the probability that the total number of heads is between 95 and 105 X Bin 200 0 5 Want P 95 X 105 Need to use normal approximation X 200 0 5 100 X 200 0 5 0 5 1 2 7 07 P 95 X 105 P X 105 P X 94 P 94 5 100 7 07 Z 105 5 100 7 07 0 7823 0 2177 0 5646 12 05 06 Review for the Final Exam 11 Practice Problem 2 Suppose 9 observations are drawn from a normal population whose standard deviation is 2 The observations are 15 9 13 11 8 12 13 8 10 At significance level 0 05 you want to determine whether the mean of the population from which this sample x 11 was taken is significantly different from 10 State the null and alternative hypotheses in symbols Compute the value of the test statistic Compute the p value Interpret the results Answers H0 10 vs Ha 10 z 1 5 and p value 0 1336 We do not reject H0 Not enough evidence 12 05 06 Review for the Final Exam 12 Practice Problem 3 Professors Smith and Jones are both planning studies of serum glucose levels in Martians The serum glucose levels are known to follow a normal distribution with a standard deviation of 5 units Each professor plans to measure a random sample of Martians and to construct a 90 confidence interval for the mean Martian serum glucose level The sample size will be Smith n 30 Jones n 300 Assume that the population of Martians is very large Q1 Would we expect Jones confidence interval to be narrower than wider than or about the same width as Smith s confidence interval Q2 Is the chance that Jones confidence interval contains less than more than or the same as the chance that Smith s confidence interval contains 12 05 06 Review for the Final Exam 13 Practice Problem 4 A multiple choice exam has 100 questions Each question has 4 possible answers of which only one is correct a What is the expected number of correct answers by sheer guesswork b What is the probability that sheer guesswork will yield at least 30 correct answers Answer a 100 1 4 25 b 30 0 5 25 P X 30 P Z P Z 1 04 0 1492 1 3 100 4 4 12 05 06 Review for the Final Exam 14 For Lectures 18 22 Review Hwk 18 22 problems 12 05 06 Review for the Final Exam 15