Solutions to Practice Test 2 Math 4753 Summer 2005
|
|
- Jemimah Terry
- 5 years ago
- Views:
Transcription
1 Solutions to Practice Test Math 4753 Summer 005 This test is worth 00 points. Questions 5 are worth 4 points each. Circle the letter of the correct answer. Each question in Question 6 9 is worth the same number of points but different parts within the questions are not necessarily worth equal amounts of points. Any work for partial credit must be shown on this sheet. Mark answers in the spaces provided. No credit will be given if work is not shown. There is no partial credit for the multiple choice questions.. A confidence interval for a proportion indicates that the proportion is likely greater than one half if: a..5 is in the confidence interval. b..5 is below the lower confidence limit. c..5 is above the upper confidence limit. Comment: For a, it is possible for the proportion to equal.5 since it is in the interval. For c, the proportion is likely less than.5 since both limits of the confidence interval are below.5. So only b is correct.. A confidence interval for a mean is wider than another confidence interval for the same mean if: a. The n is larger for the first confidence interval. b. The α for the first confidence interval is larger. c. The y for the first confidence interval is larger than that for the second confidence interval but both have the same standard deviation s (and the same α and n). Comment: For a, a larger n gives a narrow confidence interval since it gives a smaller standard deviation. For c, the width of the confidence interval depends on α, the sample size and the standard deviation s. All these are the same for the two confidence intervals in c so the width is the same ( y doesn t affect the width of the confidence interval. For b, a larger α (say.05 instead of.0) means we are looking for a less precise confidence interval (say 95% instead of 99%) and since it is less precise it will be larger. So only b is correct.
2 3. A confidence interval for the ratio of two variances shows that one of the variances is greater than the other if. a. is in the confidence interval. b. Both limits of the confidence interval are less than. c. Both limits of the confidence interval are greater than. Comment: Fir a, if ins in the confidence interval then it is possible for the ratio of variances to equal and thus for the variances to be equal. For b, if both limits are less than then the ratio of variances is less than and the variance on bottom is larger. For C, if both limits are greater than then the ratio of variances is greater than and the variance on top is larger. So both b and c are correct which makes e the correct answer. 4. For a χ -distribution, we know: a. The distribution is symmetrical. b. χ α = χ α for the same degrees of freedom. c. The area under the χ pdf above χ α is the same as the area under the χ pdf below χ α for the same degree of freedom. Comments: All χ -distributions are asymmetrical so a is false. There is no relationship between the size of the number for χ α and χ α, even with the same degree of freedom, so b is false. On the other hand, for the same degree of freedom, ( ) = α = P χ > χ ( α ) so P χ > χ ( ) = α α = P χ < χ ( α ) P χ < χ α statement. So only c is correct. and c is a true 5. If the test statistic of a hypothesis test does not fall in the rejection region for that hypothesis test then: a. We likely have made a mistake in calculating the value of the test statistic. b. We accept H 0. c. We must continue to use H 0 as a working hypothesis. Comment: The fact that the test statistic is not in the rejection region tells us nothing about whether we have made a mistake so a is not true. We can never accept H 0 as a true statement no matter what we calculation so b is not true. However, if the test statistic is not in the rejection region we must continue to use H 0. So c is true.
3 6. Suppose that a random sample of 8 OU mechanical engineering majors had an average GPA of 3.54 with a standard deviation of.5 while a random sample of 9 Texas A&M mechanical engineering majors had an average GPA of 3.0 with a standard deviation of.40. a. Find a 98% confidence interval that will allow you to decide whether the variances are the same and, if not, which is greater. We want to compare variances and the only confidence interval that allows us to do that is the one for σ. So we want a confidence interval. We want it for σ. σ σ There is no difference for large or small samples or any other factor. So the form of the confidence interval is s s g F α,( ν, ν ) σ σ s s gf α,( ν, ν ) where ν = n and ν = n.we have s = (.5) = 0.065, s = (.40) = 0.6, n = 8, n = 9, ν = 8 = 7, ν = 9 = 8, and α =.0 since we want a 98% confidence interval. We need to find F α,( ν, ν ) = F.0,( 7,8) = F.0,( 7,8) and F α,( ν, ν ) = F.0,( 8,7) = F.0,(8,7). We need to turn to Table (for.0). We see there that F.0,( 7,8) = 6.8 and F.0,(8,7) = 6.84.
4 This gives us s s g F α,( ν, ν ) σ σ s s gf α,( ν, ν ) g 6.8 σ σ g6.84 ( ) 6.8 σ σ ( ) σ σ.6788 ( ,.6788) So the 98% confidence interval for the ratio of variances is about ( 0.06,.67). b. Based on the confidence interval in a, can we assume that the variance of the GPAs of mechanical engineering students at Texas A&M is greater than that of similar students at OU? Tell how you know. Notice that in the interval ( 0.06,.67), the lower confidence limit, 0.06, is less than and the upper confidence interval,.67, is greater than. That means that is in the interval, so we could have σ <, σ = or σ >. This means that we σ σ σ could have σ < σ, σ = σ or σ > σ. Therefore, from these data and at the 98% confidence level we cannot tell whether one variance is greater than the other. 7. A production line produces rulers that are supposed to be inches long. A sample of 49 of the rulers had a mean of. and a standard deviation of.5 inches. a. Find a 95 percent confidence interval to estimate the actual mean length of the population of rulers made on the production line. This is a CI for a population mean. The form for this CI is: s x t α,ν n < µ < x + t s α where ν = n.,ν n We have y =., s =.5, n = 49, and α =.05. This gives.000 = t.05,60 < t = t < t α.ν.05,48.05,40 =.0. We use the larger value to make the interval wider (and therefore take a more conservative approach. So we have: < µ < < µ < < µ <.44 b. Given this confidence interval, is it likely that the population mean is inches as it is supposed to be? Tell how you know. We cannot tell if the population mean is inches since is in the confidence interval.
5 8. A sample of 0 OU freshmen had a mean GPA of.8 over all their courses taken in their first semester at OU. This had a variance of.5. Perform a hypothesis test at the 95 percent level to determine if the first semester GPA of all OU freshmen is less than a B (3.0). a. What is the null hypothesis? H 0 : µ = 3.0 b. What is the alternative hypothesis? H a : µ < 3.0 (one-sided test, "less than" c. What is the value of the test statistic? t = x µ 0 s n = (small sample) d. What is the rejection region (with its numerical value)? t < t n,α = t 9,.05 =.79 e. What conclusion do you draw? Reject H 0 since -.79 < f. What does this mean in terms of the problem situation? We must reject our working hypothesis that the mean GPA is 3.0 or more and conclude that it is less than A survey of 00 regular viewers of Channel 5 in Oklahoma City show that 68 believe that Gary England is God. A survey of 00 regular viewers of Channel 9 in Oklahoma City show that 68 of them also believe that Gary England is God. Given these data perform a 90 percent hypothesis to determine if the proportion of Channel 9 viewers who believe that Gary England is God is greater than the proportion of Channel 5 viewers who believe it. a. What is the null hypothesis? H 0 : p p δ 0 = 0 (Population are the regular Channel 9 viewers) b. What is the alternative hypothesis? H a : p p > δ 0 = 0 c. What is the value of the test statistic? ˆp t = ˆp = ˆp ˆq n n
6 where p ˆ = x + y n + n = because δ 0 = 0 (see Equation 9.) and we use this form of the test statistic d. What is the rejection region (with its numerical value)? t > t α = t..85 with degrees of freedom e. What conclusion do you draw? Reject H 0 because 5.58 >.85. f. What does this mean in terms of the problem situation? This means that we can conclude that H a is true and that p p > 0 or, in other words, p > p (a greater proportion of regular Channel 9 viewers believe that Gary England is God than the proportion of regular Channel 5 viewers that believe that Gary England is God. [Oh, please, Gary, forgive the Channel 5 viewers for they know not what they do]).
Hypothesis Testing One Sample Tests
STATISTICS Lecture no. 13 Department of Econometrics FEM UO Brno office 69a, tel. 973 442029 email:jiri.neubauer@unob.cz 12. 1. 2010 Tests on Mean of a Normal distribution Tests on Variance of a Normal
More informationBusiness Statistics: Lecture 8: Introduction to Estimation & Hypothesis Testing
Business Statistics: Lecture 8: Introduction to Estimation & Hypothesis Testing Agenda Introduction to Estimation Point estimation Interval estimation Introduction to Hypothesis Testing Concepts en terminology
More informationINTERVAL ESTIMATION AND HYPOTHESES TESTING
INTERVAL ESTIMATION AND HYPOTHESES TESTING 1. IDEA An interval rather than a point estimate is often of interest. Confidence intervals are thus important in empirical work. To construct interval estimates,
More informationMathematical Notation Math Introduction to Applied Statistics
Mathematical Notation Math 113 - Introduction to Applied Statistics Name : Use Word or WordPerfect to recreate the following documents. Each article is worth 10 points and can be printed and given to the
More informationMathematical Notation Math Introduction to Applied Statistics
Mathematical Notation Math 113 - Introduction to Applied Statistics Name : Use Word or WordPerfect to recreate the following documents. Each article is worth 10 points and should be emailed to the instructor
More informationSummary: the confidence interval for the mean (σ 2 known) with gaussian assumption
Summary: the confidence interval for the mean (σ known) with gaussian assumption on X Let X be a Gaussian r.v. with mean µ and variance σ. If X 1, X,..., X n is a random sample drawn from X then the confidence
More informationConfidence intervals CE 311S
CE 311S PREVIEW OF STATISTICS The first part of the class was about probability. P(H) = 0.5 P(T) = 0.5 HTTHHTTTTHHTHTHH If we know how a random process works, what will we see in the field? Preview of
More informationQUIZ 4 (CHAPTER 7) - SOLUTIONS MATH 119 SPRING 2013 KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS = 100%
QUIZ 4 (CHAPTER 7) - SOLUTIONS MATH 119 SPRING 013 KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS = 100% 1) We want to conduct a study to estimate the mean I.Q. of a pop singer s fans. We want to have 96% confidence
More information7.1 Basic Properties of Confidence Intervals
7.1 Basic Properties of Confidence Intervals What s Missing in a Point Just a single estimate What we need: how reliable it is Estimate? No idea how reliable this estimate is some measure of the variability
More informationMark Scheme (Results) Summer 2007
Mark Scheme (Results) Summer 007 GCE GCE Mathematics Statistics S3 (6691) Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH June 007 6691
More informationHypothesis testing I. - In particular, we are talking about statistical hypotheses. [get everyone s finger length!] n =
Hypothesis testing I I. What is hypothesis testing? [Note we re temporarily bouncing around in the book a lot! Things will settle down again in a week or so] - Exactly what it says. We develop a hypothesis,
More informationExam 2 (KEY) July 20, 2009
STAT 2300 Business Statistics/Summer 2009, Section 002 Exam 2 (KEY) July 20, 2009 Name: USU A#: Score: /225 Directions: This exam consists of six (6) questions, assessing material learned within Modules
More informationHarvard University. Rigorous Research in Engineering Education
Statistical Inference Kari Lock Harvard University Department of Statistics Rigorous Research in Engineering Education 12/3/09 Statistical Inference You have a sample and want to use the data collected
More informationJune 006 6691 Statistics S3 Mark Scheme Mark Scheme (Results) Summer 007 GCE GCE Mathematics Statistics S3 (6691) Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90
More informationChapter 7 Comparison of two independent samples
Chapter 7 Comparison of two independent samples 7.1 Introduction Population 1 µ σ 1 1 N 1 Sample 1 y s 1 1 n 1 Population µ σ N Sample y s n 1, : population means 1, : population standard deviations N
More informationLecture 30. DATA 8 Summer Regression Inference
DATA 8 Summer 2018 Lecture 30 Regression Inference Slides created by John DeNero (denero@berkeley.edu) and Ani Adhikari (adhikari@berkeley.edu) Contributions by Fahad Kamran (fhdkmrn@berkeley.edu) and
More informationSection 9.4. Notation. Requirements. Definition. Inferences About Two Means (Matched Pairs) Examples
Objective Section 9.4 Inferences About Two Means (Matched Pairs) Compare of two matched-paired means using two samples from each population. Hypothesis Tests and Confidence Intervals of two dependent means
More informationThe Chi-Square Distributions
MATH 183 The Chi-Square Distributions Dr. Neal, WKU The chi-square distributions can be used in statistics to analyze the standard deviation σ of a normally distributed measurement and to test the goodness
More informationSingle Sample Means. SOCY601 Alan Neustadtl
Single Sample Means SOCY601 Alan Neustadtl The Central Limit Theorem If we have a population measured by a variable with a mean µ and a standard deviation σ, and if all possible random samples of size
More informationSampling Distributions: Central Limit Theorem
Review for Exam 2 Sampling Distributions: Central Limit Theorem Conceptually, we can break up the theorem into three parts: 1. The mean (µ M ) of a population of sample means (M) is equal to the mean (µ)
More information79 Wyner Math Academy I Spring 2016
79 Wyner Math Academy I Spring 2016 CHAPTER NINE: HYPOTHESIS TESTING Review May 11 Test May 17 Research requires an understanding of underlying mathematical distributions as well as of the research methods
More informationSampling distribution of t. 2. Sampling distribution of t. 3. Example: Gas mileage investigation. II. Inferential Statistics (8) t =
2. The distribution of t values that would be obtained if a value of t were calculated for each sample mean for all possible random of a given size from a population _ t ratio: (X - µ hyp ) t s x The result
More informationFinal Exam - Solutions
Ecn 102 - Analysis of Economic Data University of California - Davis March 19, 2010 Instructor: John Parman Final Exam - Solutions You have until 5:30pm to complete this exam. Please remember to put your
More informationLAB 2. HYPOTHESIS TESTING IN THE BIOLOGICAL SCIENCES- Part 2
LAB 2. HYPOTHESIS TESTING IN THE BIOLOGICAL SCIENCES- Part 2 Data Analysis: The mean egg masses (g) of the two different types of eggs may be exactly the same, in which case you may be tempted to accept
More informationChi square test of independence
Chi square test of independence We can eyeball differences between percentages to determine whether they seem large enough to be important Better: Are differences in percentages statistically significant?
More informationDirection: This test is worth 250 points and each problem worth points. DO ANY SIX
Term Test 3 December 5, 2003 Name Math 52 Student Number Direction: This test is worth 250 points and each problem worth 4 points DO ANY SIX PROBLEMS You are required to complete this test within 50 minutes
More information2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
More informationD. A 90% confidence interval for the ratio of two variances is (.023,1.99). Based on the confidence interval you will fail to reject H 0 =!
SMAM 314 Review for Exam 3 1. Mark the following statements true (T) or false(f) A. A null hypothesis that is rejected at α=.01 will always be rejected at α=.05. Β. One hundred 90% confidence intervals
More informationChapter 5: HYPOTHESIS TESTING
MATH411: Applied Statistics Dr. YU, Chi Wai Chapter 5: HYPOTHESIS TESTING 1 WHAT IS HYPOTHESIS TESTING? As its name indicates, it is about a test of hypothesis. To be more precise, we would first translate
More informationi=1 X i/n i=1 (X i X) 2 /(n 1). Find the constant c so that the statistic c(x X n+1 )/S has a t-distribution. If n = 8, determine k such that
Math 47 Homework Assignment 4 Problem 411 Let X 1, X,, X n, X n+1 be a random sample of size n + 1, n > 1, from a distribution that is N(µ, σ ) Let X = n i=1 X i/n and S = n i=1 (X i X) /(n 1) Find the
More informationFirst we look at some terms to be used in this section.
8 Hypothesis Testing 8.1 Introduction MATH1015 Biostatistics Week 8 In Chapter 7, we ve studied the estimation of parameters, point or interval estimates. The construction of CI relies on the sampling
More informationSTAT Chapter 8: Hypothesis Tests
STAT 515 -- Chapter 8: Hypothesis Tests CIs are possibly the most useful forms of inference because they give a range of reasonable values for a parameter. But sometimes we want to know whether one particular
More informationEC2001 Econometrics 1 Dr. Jose Olmo Room D309
EC2001 Econometrics 1 Dr. Jose Olmo Room D309 J.Olmo@City.ac.uk 1 Revision of Statistical Inference 1.1 Sample, observations, population A sample is a number of observations drawn from a population. Population:
More informationDesign of Engineering Experiments Part 2 Basic Statistical Concepts Simple comparative experiments
Design of Engineering Experiments Part 2 Basic Statistical Concepts Simple comparative experiments The hypothesis testing framework The two-sample t-test Checking assumptions, validity Comparing more that
More informationLecture 12: Small Sample Intervals Based on a Normal Population Distribution
Lecture 12: Small Sample Intervals Based on a Normal Population MSU-STT-351-Sum-17B (P. Vellaisamy: MSU-STT-351-Sum-17B) Probability & Statistics for Engineers 1 / 24 In this lecture, we will discuss (i)
More informationThe Components of a Statistical Hypothesis Testing Problem
Statistical Inference: Recall from chapter 5 that statistical inference is the use of a subset of a population (the sample) to draw conclusions about the entire population. In chapter 5 we studied one
More informationStatistical Inference
Statistical Inference Classical and Bayesian Methods Revision Class for Midterm Exam AMS-UCSC Th Feb 9, 2012 Winter 2012. Session 1 (Revision Class) AMS-132/206 Th Feb 9, 2012 1 / 23 Topics Topics We will
More informationChapter 10: Inferences based on two samples
November 16 th, 2017 Overview Week 1 Week 2 Week 4 Week 7 Week 10 Week 12 Chapter 1: Descriptive statistics Chapter 6: Statistics and Sampling Distributions Chapter 7: Point Estimation Chapter 8: Confidence
More informationDifference between means - t-test /25
Difference between means - t-test 1 Discussion Question p492 Ex 9-4 p492 1-3, 6-8, 12 Assume all variances are not equal. Ignore the test for variance. 2 Students will perform hypothesis tests for two
More informationStatistical Intervals (One sample) (Chs )
7 Statistical Intervals (One sample) (Chs 8.1-8.3) Confidence Intervals The CLT tells us that as the sample size n increases, the sample mean X is close to normally distributed with expected value µ and
More informationCan you tell the relationship between students SAT scores and their college grades?
Correlation One Challenge Can you tell the relationship between students SAT scores and their college grades? A: The higher SAT scores are, the better GPA may be. B: The higher SAT scores are, the lower
More informationChapter 7: Statistical Inference (Two Samples)
Chapter 7: Statistical Inference (Two Samples) Shiwen Shen University of South Carolina 2016 Fall Section 003 1 / 41 Motivation of Inference on Two Samples Until now we have been mainly interested in a
More informationStat 231 Exam 2 Fall 2013
Stat 231 Exam 2 Fall 2013 I have neither given nor received unauthorized assistance on this exam. Name Signed Date Name Printed 1 1. Some IE 361 students worked with a manufacturer on quantifying the capability
More informationGeneral Certificate of Education Advanced Level Examination June 2014
General Certificate of Education Advanced Level Examination June 2014 Biology BIO6T/Q14/task Unit 6T A2 Investigative Skills Assignment Task Sheet Introduction Investigating populations You will use leaves
More informationPermutation Tests. Noa Haas Statistics M.Sc. Seminar, Spring 2017 Bootstrap and Resampling Methods
Permutation Tests Noa Haas Statistics M.Sc. Seminar, Spring 2017 Bootstrap and Resampling Methods The Two-Sample Problem We observe two independent random samples: F z = z 1, z 2,, z n independently of
More informationChapter 10: Analysis of variance (ANOVA)
Chapter 10: Analysis of variance (ANOVA) ANOVA (Analysis of variance) is a collection of techniques for dealing with more general experiments than the previous one-sample or two-sample tests. We first
More informationReview: General Approach to Hypothesis Testing. 1. Define the research question and formulate the appropriate null and alternative hypotheses.
1 Review: Let X 1, X,..., X n denote n independent random variables sampled from some distribution might not be normal!) with mean µ) and standard deviation σ). Then X µ σ n In other words, X is approximately
More informationPOLI 443 Applied Political Research
POLI 443 Applied Political Research Session 6: Tests of Hypotheses Contingency Analysis Lecturer: Prof. A. Essuman-Johnson, Dept. of Political Science Contact Information: aessuman-johnson@ug.edu.gh College
More informationy ˆ i = ˆ " T u i ( i th fitted value or i th fit)
1 2 INFERENCE FOR MULTIPLE LINEAR REGRESSION Recall Terminology: p predictors x 1, x 2,, x p Some might be indicator variables for categorical variables) k-1 non-constant terms u 1, u 2,, u k-1 Each u
More informationECO220Y Review and Introduction to Hypothesis Testing Readings: Chapter 12
ECO220Y Review and Introduction to Hypothesis Testing Readings: Chapter 12 Winter 2012 Lecture 13 (Winter 2011) Estimation Lecture 13 1 / 33 Review of Main Concepts Sampling Distribution of Sample Mean
More informationApplied Statistics I
Applied Statistics I Liang Zhang Department of Mathematics, University of Utah July 17, 2008 Liang Zhang (UofU) Applied Statistics I July 17, 2008 1 / 23 Large-Sample Confidence Intervals Liang Zhang (UofU)
More informationTest 3 Practice Test A. NOTE: Ignore Q10 (not covered)
Test 3 Practice Test A NOTE: Ignore Q10 (not covered) MA 180/418 Midterm Test 3, Version A Fall 2010 Student Name (PRINT):............................................. Student Signature:...................................................
More informationSTA Module 10 Comparing Two Proportions
STA 2023 Module 10 Comparing Two Proportions Learning Objectives Upon completing this module, you should be able to: 1. Perform large-sample inferences (hypothesis test and confidence intervals) to compare
More informationThe t-distribution. Patrick Breheny. October 13. z tests The χ 2 -distribution The t-distribution Summary
Patrick Breheny October 13 Patrick Breheny Biostatistical Methods I (BIOS 5710) 1/25 Introduction Introduction What s wrong with z-tests? So far we ve (thoroughly!) discussed how to carry out hypothesis
More informationCHAPTER 9, 10. Similar to a courtroom trial. In trying a person for a crime, the jury needs to decide between one of two possibilities:
CHAPTER 9, 10 Hypothesis Testing Similar to a courtroom trial. In trying a person for a crime, the jury needs to decide between one of two possibilities: The person is guilty. The person is innocent. To
More informationCBA4 is live in practice mode this week exam mode from Saturday!
Announcements CBA4 is live in practice mode this week exam mode from Saturday! Material covered: Confidence intervals (both cases) 1 sample hypothesis tests (both cases) Hypothesis tests for 2 means as
More information1 Statistical inference for a population mean
1 Statistical inference for a population mean 1. Inference for a large sample, known variance Suppose X 1,..., X n represents a large random sample of data from a population with unknown mean µ and known
More informationName: Exam: In-term Two Page: 1 of 8 Date: 12/07/2018. University of Texas at Austin, Department of Mathematics M358K - Applied Statistics TRUE/FALSE
Exam: In-term Two Page: 1 of 8 Date: 12/07/2018 Name: TRUE/FALSE 1.1 TRUE FALSE University of Texas at Austin, Department of Mathematics M358K - Applied Statistics MULTIPLE CHOICE 1.2 TRUE FALSE 1.3 TRUE
More informationCh. 7. One sample hypothesis tests for µ and σ
Ch. 7. One sample hypothesis tests for µ and σ Prof. Tesler Math 18 Winter 2019 Prof. Tesler Ch. 7: One sample hypoth. tests for µ, σ Math 18 / Winter 2019 1 / 23 Introduction Data Consider the SAT math
More informationBusiness Statistics. Lecture 10: Course Review
Business Statistics Lecture 10: Course Review 1 Descriptive Statistics for Continuous Data Numerical Summaries Location: mean, median Spread or variability: variance, standard deviation, range, percentiles,
More informationChapter 5 Confidence Intervals
Chapter 5 Confidence Intervals Confidence Intervals about a Population Mean, σ, Known Abbas Motamedi Tennessee Tech University A point estimate: a single number, calculated from a set of data, that is
More informationHypothesis testing (cont d)
Hypothesis testing (cont d) Ulrich Heintz Brown University 4/12/2016 Ulrich Heintz - PHYS 1560 Lecture 11 1 Hypothesis testing Is our hypothesis about the fundamental physics correct? We will not be able
More informationThe Chi-Square Distributions
MATH 03 The Chi-Square Distributions Dr. Neal, Spring 009 The chi-square distributions can be used in statistics to analyze the standard deviation of a normally distributed measurement and to test the
More informationObjectives Simple linear regression. Statistical model for linear regression. Estimating the regression parameters
Objectives 10.1 Simple linear regression Statistical model for linear regression Estimating the regression parameters Confidence interval for regression parameters Significance test for the slope Confidence
More informationHOMEWORK ANALYSIS #3 - WATER AVAILABILITY (DATA FROM WEISBERG 2014)
HOMEWORK ANALYSIS #3 - WATER AVAILABILITY (DATA FROM WEISBERG 2014) 1. In your own words, summarize the overarching problem and any specific questions that need to be answered using the water data. Discuss
More informationSoc3811 Second Midterm Exam
Soc38 Second Midterm Exam SEMI-OPE OTE: One sheet of paper, signed & turned in with exam booklet Bring our Own Pencil with Eraser and a Hand Calculator! Standardized Scores & Probability If we know the
More informationRelax and good luck! STP 231 Example EXAM #2. Instructor: Ela Jackiewicz
STP 31 Example EXAM # Instructor: Ela Jackiewicz Honor Statement: I have neither given nor received information regarding this exam, and I will not do so until all exams have been graded and returned.
More informationStatistical Inference for Means
Statistical Inference for Means Jamie Monogan University of Georgia February 18, 2011 Jamie Monogan (UGA) Statistical Inference for Means February 18, 2011 1 / 19 Objectives By the end of this meeting,
More informationISyE 2028 Basic Statistical Methods - Fall 2015 Bonus Project: Big Data Analytics Final Report
ISyE 2028 Basic Statistical Methods - Fall 2015 Bonus Project: Big Data Analytics Final Report Chrystelle_Nare STEM vs. non STEM majors academic performance at Georgia Tech Throughout college, and after
More informationChi square test of independence
Chi square test of independence Eyeball differences between percentages: large enough to be important Better: Are they statistically significant? Statistical significance: are observed differences significantly
More informationProblem Set 4 - Solutions
Problem Set 4 - Solutions Econ-310, Spring 004 8. a. If we wish to test the research hypothesis that the mean GHQ score for all unemployed men exceeds 10, we test: H 0 : µ 10 H a : µ > 10 This is a one-tailed
More informationMath 1040 Final Exam Form A Introduction to Statistics Fall Semester 2010
Math 1040 Final Exam Form A Introduction to Statistics Fall Semester 2010 Instructor Name Time Limit: 120 minutes Any calculator is okay. Necessary tables and formulas are attached to the back of the exam.
More informationIntroductory Econometrics
Session 4 - Testing hypotheses Roland Sciences Po July 2011 Motivation After estimation, delivering information involves testing hypotheses Did this drug had any effect on the survival rate? Is this drug
More informationEcon 325: Introduction to Empirical Economics
Econ 325: Introduction to Empirical Economics Chapter 9 Hypothesis Testing: Single Population Ch. 9-1 9.1 What is a Hypothesis? A hypothesis is a claim (assumption) about a population parameter: population
More informationChapter 12: Estimation
Chapter 12: Estimation Estimation In general terms, estimation uses a sample statistic as the basis for estimating the value of the corresponding population parameter. Although estimation and hypothesis
More informationChapter. Hypothesis Testing with Two Samples. Copyright 2015, 2012, and 2009 Pearson Education, Inc. 1
Chapter 8 Hypothesis Testing with Two Samples Copyright 2015, 2012, and 2009 Pearson Education, Inc 1 Two Sample Hypothesis Test Compares two parameters from two populations Sampling methods: Independent
More informationDescriptive Statistics
Descriptive Statistics Once an experiment is carried out and the results are measured, the researcher has to decide whether the results of the treatments are different. This would be easy if the results
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. describes the.
Practice Test 3 Math 1342 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The term z α/2 σn describes the. 1) A) maximum error of estimate
More informationHypothesis Testing and Confidence Intervals (Part 2): Cohen s d, Logic of Testing, and Confidence Intervals
Hypothesis Testing and Confidence Intervals (Part 2): Cohen s d, Logic of Testing, and Confidence Intervals Lecture 9 Justin Kern April 9, 2018 Measuring Effect Size: Cohen s d Simply finding whether a
More informationInference for Proportions, Variance and Standard Deviation
Inference for Proportions, Variance and Standard Deviation Sections 7.10 & 7.6 Cathy Poliak, Ph.D. cathy@math.uh.edu Office Fleming 11c Department of Mathematics University of Houston Lecture 12 Cathy
More informationAlgebra 2 CP Semester 1 PRACTICE Exam
Algebra 2 CP Semester 1 PRACTICE Exam NAME DATE HR You may use a calculator. Please show all work directly on this test. You may write on the test. GOOD LUCK! THIS IS JUST PRACTICE GIVE YOURSELF 45 MINUTES
More informationChapter 27 Summary Inferences for Regression
Chapter 7 Summary Inferences for Regression What have we learned? We have now applied inference to regression models. Like in all inference situations, there are conditions that we must check. We can test
More informationIs there a connection between gender, maths grade, hair colour and eye colour? Contents
5 Sample project This Maths Studies project has been graded by a moderator. As you read through it, you will see comments from the moderator in boxes like this: At the end of the sample project is a summary
More information4.1 Hypothesis Testing
4.1 Hypothesis Testing z-test for a single value double-sided and single-sided z-test for one average z-test for two averages double-sided and single-sided t-test for one average the F-parameter and F-table
More informationStatistical inference
Statistical inference Contents 1. Main definitions 2. Estimation 3. Testing L. Trapani MSc Induction - Statistical inference 1 1 Introduction: definition and preliminary theory In this chapter, we shall
More information7 Estimation. 7.1 Population and Sample (P.91-92)
7 Estimation MATH1015 Biostatistics Week 7 7.1 Population and Sample (P.91-92) Suppose that we wish to study a particular health problem in Australia, for example, the average serum cholesterol level for
More informationMidterm 2 - Solutions
Ecn 102 - Analysis of Economic Data University of California - Davis February 23, 2010 Instructor: John Parman Midterm 2 - Solutions You have until 10:20am to complete this exam. Please remember to put
More informationOne sided tests. An example of a two sided alternative is what we ve been using for our two sample tests:
One sided tests So far all of our tests have been two sided. While this may be a bit easier to understand, this is often not the best way to do a hypothesis test. One simple thing that we can do to get
More informationThe point value of each problem is in the left-hand margin. You must show your work to receive any credit, except on problems 1 & 2. Work neatly.
Introduction to Statistics Math 1040 Sample Exam III Chapters 8-10 4 Problem Pages 3 Formula/Table Pages Time Limit: 90 Minutes 1 No Scratch Paper Calculator Allowed: Scientific Name: The point value of
More information9.5 t test: one μ, σ unknown
GOALS: 1. Recognize the assumptions for a 1 mean t test (srs, nd or large sample size, population stdev. NOT known). 2. Understand that the actual p value (area in the tail past the test statistic) is
More informationThe Purpose of Hypothesis Testing
Section 8 1A:! An Introduction to Hypothesis Testing The Purpose of Hypothesis Testing See s Candy states that a box of it s candy weighs 16 oz. They do not mean that every single box weights exactly 16
More informationLecture 26: Chapter 10, Section 2 Inference for Quantitative Variable Confidence Interval with t
Lecture 26: Chapter 10, Section 2 Inference for Quantitative Variable Confidence Interval with t t Confidence Interval for Population Mean Comparing z and t Confidence Intervals When neither z nor t Applies
More informationChapter 1A -- Real Numbers. iff. Math Symbols: Sets of Numbers
Fry Texas A&M University! Fall 2016! Math 150 Notes! Section 1A! Page 1 Chapter 1A -- Real Numbers Math Symbols: iff or Example: Let A = {2, 4, 6, 8, 10, 12, 14, 16,...} and let B = {3, 6, 9, 12, 15, 18,
More informationStat 135 Fall 2013 FINAL EXAM December 18, 2013
Stat 135 Fall 2013 FINAL EXAM December 18, 2013 Name: Person on right SID: Person on left There will be one, double sided, handwritten, 8.5in x 11in page of notes allowed during the exam. The exam is closed
More informationM(t) = 1 t. (1 t), 6 M (0) = 20 P (95. X i 110) i=1
Math 66/566 - Midterm Solutions NOTE: These solutions are for both the 66 and 566 exam. The problems are the same until questions and 5. 1. The moment generating function of a random variable X is M(t)
More informationSoc 3811 Basic Social Statistics Second Midterm Exam Spring Your Name [50 points]: ID #: ANSWERS
Soc 3811 Basic Social Statistics Second idterm Exam Spring 010 our Name [50 points]: ID #: INSTRUCTIONS: ANSERS (A) rite your name on the line at top front of every sheet. (B) If you use a page of notes
More information23. MORE HYPOTHESIS TESTING
23. MORE HYPOTHESIS TESTING The Logic Behind Hypothesis Testing For simplicity, consider testing H 0 : µ = µ 0 against the two-sided alternative H A : µ µ 0. Even if H 0 is true (so that the expectation
More information10.4 Hypothesis Testing: Two Independent Samples Proportion
10.4 Hypothesis Testing: Two Independent Samples Proportion Example 3: Smoking cigarettes has been known to cause cancer and other ailments. One politician believes that a higher tax should be imposed
More information1; (f) H 0 : = 55 db, H 1 : < 55.
Reference: Chapter 8 of J. L. Devore s 8 th Edition By S. Maghsoodloo TESTING a STATISTICAL HYPOTHESIS A statistical hypothesis is an assumption about the frequency function(s) (i.e., pmf or pdf) of one
More informationPractice Questions: Statistics W1111, Fall Solutions
Practice Questions: Statistics W, Fall 9 Solutions Question.. The standard deviation of Z is 89... P(=6) =..3. is definitely inside of a 95% confidence interval for..4. (a) YES (b) YES (c) NO (d) NO Questions
More information