The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STOR 155 Introductory Statistics Review for the Final Exam Summer 2011 6 10 11 Review for the Final Exam 1 Final Exam Format Monday 6 13 8 11 am Closed book closed notes One formula sheet double sided Calculator Scantron and 2 pencils Tables will be provided Between 40 50 multiple choice questions about a half based on materials covered after the 2nd midterm 6 10 11 Review for the Final Exam 2 Suggestions for your review Read the lecture notes carefully Go over homework problems previous review problems practice problems in this final review practice midterms and final Solve the problems yourself 6 10 11 Review for the Final Exam 3 What have we learned in STOR 155 Basic data analysis techniques Simple linear regression Elementary probability Sampling distributions Point estimation confidence intervals Hypothesis testing z test t test 6 10 11 Review for the Final Exam 4 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 6 10 11 Review for the Final Exam 5 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 6 10 11 Review for the Final Exam 6 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 6 10 11 Review for the Final Exam 7 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 approx normal for large samples 6 10 11 Review for the Final Exam 8 Road map for CI and HT Lectures 16 21 1 sample or two samples 1 sample or p 2 samples 1 2 or p 1 p 2 CI or HT For p 1 p 2 use SE D or SEDp Ha 1 sided or 2 sided Which P value to calculate Z table or t table Decision reject or accept H0 CI what is the margin of error HT which 4 steps Relationship between CI and HT 6 10 11 Review for the Final Exam 9 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 6 10 11 Review for the Final Exam 10 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 6 10 11 Review for the Final Exam 11 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 6 10 11 Review for the Final Exam 12 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 30 0 5 25 P X 30 P Z P Z 1 04 0 1492 1 3 100 4 4 b 6 10 11 Review for the Final Exam 13
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