6/11/10 Review for the Final Exam 1STOR 155 Introductory StatisticsReview for the Final Exam The UNIVERSITY of NORTH CAROLINAat CHAPEL HILL6/11/10 Review for the Final Exam 2Final Exam Format• Monday, 6/14, 8 --- 11 am • Closed-book, closed-notes• One formula sheet • Calculator • Scantron and #2 pencils • Tables will be provided• Between 40 & 50 multiple choice questions --- at least a half based on materials covered after the 2ndmidterm6/11/10 Review for the Final Exam 3Suggestions for your review• Read the lecture notes carefully.• Go over – homework problems – previous review problems– practice problems in this final reviewand in those sample exams (Solve the problems yourself !)6/11/10 Review for the Final Exam 4What 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)6/11/10 Review for the Final Exam 5Review 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 calculation6/11/10 Review for the Final Exam 6Review 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 variables6/11/10 Review for the Final Exam 7Review 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 & variances6/11/10 Review for the Final Exam 8Review of Chapter 5• Binomial distribution– Sampling distribution for counts and proportions– Table C, mean, standard deviation– Normal approximation (continuity correction)• Sampling distribution ofXsamples. largefor normal approx. is nonnormal, is If (ii) normal. is normal, isIf )i(.2 ;.122XXXXnXXXX6/11/10 Review for the Final Exam 9Road map for CI and HT (Lectures 16 – 22)• 1 sample or two samples?• 1 sample: or ?• 2 samples: or ?• CI or HT ?• For : use or ? • : 1-sided or 2-sided?• Which P-value to calculate ? Z-table or t-table ?• Decision: reject or accept ?• CI: what is the margin of error?• HT: which 4 steps ?• Relationship between CI and HT ?pöö1à ö2p1à p2p1à p2SEDSEDpHaH06/11/10 Review for the Final Exam 10Practice 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 = 0.5646.6/11/10 Review for the Final Exam 11Practice 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 ( ) 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: µ = 10 vs. Ha: µ ≠ 10. – z = 1.5 and p-value = 0.1336– We do not reject H0… Not enough evidence.11x6/11/10 Review for the Final Exam 12Practice 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 asSmith'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 ?6/11/10 Review for the Final Exam 13Practice 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).1492.0)04.1()4341100255.030()30(
View Full Document
Unlocking...