Hypothesis Tests for a Population Proportion
|
|
- Whitney Leonard
- 7 years ago
- Views:
Transcription
1 Hypothesis Tests for a Population Proportion MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2015
2 Review: Steps of Hypothesis Testing 1. A statement is made regarding the nature of the population (usually about µ or p). 2. Evidence (sample data) is collected to test the statement. 3. The data are analyzed to assess the plausibility of the statement.
3 Background Hypothesis testing about the population proportion is carried out very similarly to the familiar method for hypothesis testing involving the population mean. Assumptions: 1. Simple random sample of size n 0.05N is collected. 2. If p 0 is the assumed value of the population proportion, then np 0 (1 p 0 ) The test statistic will be calculated as z = ˆp p 0 p 0 (1 p 0 ) n.
4 Methods There are three equivalent methods for conducting the hypothesis test: 1. Classical approach, 2. P-Value approach, 3. Confidence interval approach.
5 Classical Approach 1. State the null and alternative hypotheses. H 0 : p = p 0 H 1 : p, <, > p 0 2. Select a level of significance α. 3. Calculate the test statistic: z = ˆp p 0 p 0 (1 p 0 ) n 4. If the test statistic falls in the critical region, reject H State the conclusion..
6 Critical Region (1 of 2) Test Two-tailed CV ±z α/2 CR
7 Critical Region (2 of 2) Test Left-tailed Right-tailed CV z α z α CR
8 Remarks If the sample mean is too many standard deviations away from the mean stated in the null hypothesis, we reject the null hypothesis. When the results observed in the sample are unlikely to have occurred under the assumption of the null hypothesis, we say the result is statistically significant. The classical approach is robust in the sense that small departures from the assumption of a normally distributed population do not usually affect the result of the test.
9 Classical Approach (1 of 3) An insurance company states that 90% of its claims are settled within 30 days. A consumer group selected a simple random sample of 75 of the company s claims to test this statement. The consumer group found that 55 of the claims were settled within 30 days. At the 0.05 significance level, test the company s claim that 90% of its claims are settled within 30 days.
10 Classical Approach (1 of 3) An insurance company states that 90% of its claims are settled within 30 days. A consumer group selected a simple random sample of 75 of the company s claims to test this statement. The consumer group found that 55 of the claims were settled within 30 days. At the 0.05 significance level, test the company s claim that 90% of its claims are settled within 30 days. Remark: the phrase 90% of claims implies 90% or more. The consumer group s hypothesis is that less than 90% of claims are settled in 30 days.
11 Claasical Approach (2 of 3) H 0 : p = 0.90 H 1 : p < 0.90 (left-tailed test) α = 0.05, z α = z 0.05 = Test statistic: z = 55/ (1 0.90) 75 = 4.811
12 Example (3 of 3) TS: z Decision: reject H 0. Conclusion: the sample data warrants rejection of the claim that 90% of the company s insurance claims are settled within 30 days (at the α = 0.05 significance level).
13 P-Value Approach (1 of 3) A politician claims that she will receive at least 60% of the votes in an upcoming election. The results of a simple random sample of 100 voters showed that 58 of those sampled will vote for her. Test the politician s claim at the 0.05 level of significance.
14 P-Value Approach (1 of 3) A politician claims that she will receive at least 60% of the votes in an upcoming election. The results of a simple random sample of 100 voters showed that 58 of those sampled will vote for her. Test the politician s claim at the 0.05 level of significance. Remark: the politician is stating that she will receive 60% or more of the votes. The alternative is that she will receive less than 60% of the votes.
15 P-Value Approach (2 of 3) H 0 : p = 0.60 H 1 : p < 0.60 (left-tailed test) α = 0.05, z α = z 0.05 = Test statistic: z = 58/ (1 0.60) 100 = 0.41
16 P-Value Approach (3 of 3) P-value: Decision: do not reject H 0. P(Z < 0.41) = = α Conclusion: the sample data do not warrant rejection of the claim that the politician will receive 60% of the vote (at the α = 0.05 level of significance with P-value = ).
17 Classical Approach (1 of 3) The full-time student body of a college is 50% men and 50% women. Suppose an introductory chemistry class contains 30 men and 20 women. Does this sample provide sufficient evidence at the 0.05 significance level to reject the hypothesis that the proportions of male and female students who take this course are the same as in the general student body?
18 Classical Approach (2 of 3) H 0 : p = 0.50 H 1 : p 0.50 (two-tailed test) α = 0.05, α/2 = 0.025, ±z α/2 = ±1.96 Test statistic: z = 30/ (1 0.50) 50 = 1.41
19 Classical Approach (3 of 3) TS: z Decision: fail to reject H 0. Conclusion: at the α = 0.05 significance level, the sample data does not warrant rejection of the claim that the proportions of male and female students in the introductory chemistry class is the same as in the general student body.
20 P-Value Approach (1 of 3) The popularity of personal watercraft (also known as jet skis) continues to increase, despite the apparent danger associated with their use. A sample of 54 watercraft accidents reported to the Nebraska Game and Parks Commission in 1997 revealed that 85% of them involved personal watercraft even though only 8% of the motorized boats registered in the state are personal watercraft. Suppose the national average proportion of watercraft accidents in 1997 involving personal watercraft was 78%. Does the watercraft accident rate in Nebraska exceed the rate in the nation? Use the 0.01 level of significance.
21 P-Value Approach (2 of 3) H 0 : p = 0.78 H 1 : p > 0.78 (right-tailed test) α = 0.01, z α = 2.33 Test statistic: z = (1 0.78) 54 = 1.24
22 P-Value Approach (3 of 3) P-value: P(Z > 1.24) = 1 P(Z < 1.24) Decision: do not reject H 0. = = = α Conclusion: at the α = 0.01 significance level, the sample data do not support that claim that the watercraft accident rate in Nebraska exceeds the rate in the nation (P-value = ).
Chapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing
Chapter 8 Hypothesis Testing 1 Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing 8-3 Testing a Claim About a Proportion 8-5 Testing a Claim About a Mean: s Not Known 8-6 Testing
More informationStats Review Chapters 9-10
Stats Review Chapters 9-10 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test
More informationOnline 12 - Sections 9.1 and 9.2-Doug Ensley
Student: Date: Instructor: Doug Ensley Course: MAT117 01 Applied Statistics - Ensley Assignment: Online 12 - Sections 9.1 and 9.2 1. Does a P-value of 0.001 give strong evidence or not especially strong
More informationHypothesis Testing --- One Mean
Hypothesis Testing --- One Mean A hypothesis is simply a statement that something is true. Typically, there are two hypotheses in a hypothesis test: the null, and the alternative. Null Hypothesis The hypothesis
More informationSection 7.1. Introduction to Hypothesis Testing. Schrodinger s cat quantum mechanics thought experiment (1935)
Section 7.1 Introduction to Hypothesis Testing Schrodinger s cat quantum mechanics thought experiment (1935) Statistical Hypotheses A statistical hypothesis is a claim about a population. Null hypothesis
More informationMath 251, Review Questions for Test 3 Rough Answers
Math 251, Review Questions for Test 3 Rough Answers 1. (Review of some terminology from Section 7.1) In a state with 459,341 voters, a poll of 2300 voters finds that 45 percent support the Republican candidate,
More informationGeneral Method: Difference of Means. 3. Calculate df: either Welch-Satterthwaite formula or simpler df = min(n 1, n 2 ) 1.
General Method: Difference of Means 1. Calculate x 1, x 2, SE 1, SE 2. 2. Combined SE = SE1 2 + SE2 2. ASSUMES INDEPENDENT SAMPLES. 3. Calculate df: either Welch-Satterthwaite formula or simpler df = min(n
More informationAn Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10- TWO-SAMPLE TESTS
The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 130) Spring Semester 011 Chapter 10- TWO-SAMPLE TESTS Practice
More information3.4 Statistical inference for 2 populations based on two samples
3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted
More informationUnit 26 Estimation with Confidence Intervals
Unit 26 Estimation with Confidence Intervals Objectives: To see how confidence intervals are used to estimate a population proportion, a population mean, a difference in population proportions, or a difference
More informationBA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394
BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394 1. Does vigorous exercise affect concentration? In general, the time needed for people to complete
More informationIntroduction to Hypothesis Testing OPRE 6301
Introduction to Hypothesis Testing OPRE 6301 Motivation... The purpose of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief, or hypothesis, about
More informationAP STATISTICS (Warm-Up Exercises)
AP STATISTICS (Warm-Up Exercises) 1. Describe the distribution of ages in a city: 2. Graph a box plot on your calculator for the following test scores: {90, 80, 96, 54, 80, 95, 100, 75, 87, 62, 65, 85,
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Sample Practice problems - chapter 12-1 and 2 proportions for inference - Z Distributions Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide
More informationStatistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice!
Statistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice!) Part A - Multiple Choice Indicate the best choice
More informationCONTENTS OF DAY 2. II. Why Random Sampling is Important 9 A myth, an urban legend, and the real reason NOTES FOR SUMMER STATISTICS INSTITUTE COURSE
1 2 CONTENTS OF DAY 2 I. More Precise Definition of Simple Random Sample 3 Connection with independent random variables 3 Problems with small populations 8 II. Why Random Sampling is Important 9 A myth,
More informationName: Date: Use the following to answer questions 3-4:
Name: Date: 1. Determine whether each of the following statements is true or false. A) The margin of error for a 95% confidence interval for the mean increases as the sample size increases. B) The margin
More informationA) 0.1554 B) 0.0557 C) 0.0750 D) 0.0777
Math 210 - Exam 4 - Sample Exam 1) What is the p-value for testing H1: µ < 90 if the test statistic is t=-1.592 and n=8? A) 0.1554 B) 0.0557 C) 0.0750 D) 0.0777 2) The owner of a football team claims that
More informationSTAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico. Fall 2013
STAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico Fall 2013 CHAPTER 18 INFERENCE ABOUT A POPULATION MEAN. Conditions for Inference about mean
More information5/31/2013. Chapter 8 Hypothesis Testing. Hypothesis Testing. Hypothesis Testing. Outline. Objectives. Objectives
C H 8A P T E R Outline 8 1 Steps in Traditional Method 8 2 z Test for a Mean 8 3 t Test for a Mean 8 4 z Test for a Proportion 8 6 Confidence Intervals and Copyright 2013 The McGraw Hill Companies, Inc.
More informationMath 108 Exam 3 Solutions Spring 00
Math 108 Exam 3 Solutions Spring 00 1. An ecologist studying acid rain takes measurements of the ph in 12 randomly selected Adirondack lakes. The results are as follows: 3.0 6.5 5.0 4.2 5.5 4.7 3.4 6.8
More informationRegression Analysis: A Complete Example
Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty
More informationSection 8-1 Pg. 410 Exercises 12,13
Section 8- Pg. 4 Exercises 2,3 2. Using the z table, find the critical value for each. a) α=.5, two-tailed test, answer: -.96,.96 b) α=., left-tailed test, answer: -2.33, 2.33 c) α=.5, right-tailed test,
More informationChapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion
Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion Learning Objectives Upon successful completion of Chapter 8, you will be able to: Understand terms. State the null and alternative
More informationReview #2. Statistics
Review #2 Statistics Find the mean of the given probability distribution. 1) x P(x) 0 0.19 1 0.37 2 0.16 3 0.26 4 0.02 A) 1.64 B) 1.45 C) 1.55 D) 1.74 2) The number of golf balls ordered by customers of
More informationC. The null hypothesis is not rejected when the alternative hypothesis is true. A. population parameters.
Sample Multiple Choice Questions for the material since Midterm 2. Sample questions from Midterms and 2 are also representative of questions that may appear on the final exam.. A randomly selected sample
More informationExperimental Design. Power and Sample Size Determination. Proportions. Proportions. Confidence Interval for p. The Binomial Test
Experimental Design Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 To this point in the semester, we have largely
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Ch. 10 Chi SquareTests and the F-Distribution 10.1 Goodness of Fit 1 Find Expected Frequencies Provide an appropriate response. 1) The frequency distribution shows the ages for a sample of 100 employees.
More informationBA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420
BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420 1. Which of the following will increase the value of the power in a statistical test
More informationChapter 7 TEST OF HYPOTHESIS
Chapter 7 TEST OF HYPOTHESIS In a certain perspective, we can view hypothesis testing just like a jury in a court trial. In a jury trial, the null hypothesis is similar to the jury making a decision of
More informationMind on Statistics. Chapter 4
Mind on Statistics Chapter 4 Sections 4.1 Questions 1 to 4: The table below shows the counts by gender and highest degree attained for 498 respondents in the General Social Survey. Highest Degree Gender
More informationAssociation Between Variables
Contents 11 Association Between Variables 767 11.1 Introduction............................ 767 11.1.1 Measure of Association................. 768 11.1.2 Chapter Summary.................... 769 11.2 Chi
More informationMind on Statistics. Chapter 12
Mind on Statistics Chapter 12 Sections 12.1 Questions 1 to 6: For each statement, determine if the statement is a typical null hypothesis (H 0 ) or alternative hypothesis (H a ). 1. There is no difference
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationUniversity of Chicago Graduate School of Business. Business 41000: Business Statistics Solution Key
Name: OUTLINE SOLUTIONS University of Chicago Graduate School of Business Business 41000: Business Statistics Solution Key Special Notes: 1. This is a closed-book exam. You may use an 8 11 piece of paper
More informationHYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...
HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men
More informationChapter 23 Inferences About Means
Chapter 23 Inferences About Means Chapter 23 - Inferences About Means 391 Chapter 23 Solutions to Class Examples 1. See Class Example 1. 2. We want to know if the mean battery lifespan exceeds the 300-minute
More informationStatistics 2014 Scoring Guidelines
AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home
More informationIntroduction to Hypothesis Testing
I. Terms, Concepts. Introduction to Hypothesis Testing A. In general, we do not know the true value of population parameters - they must be estimated. However, we do have hypotheses about what the true
More informationSocial Studies 201 Notes for November 19, 2003
1 Social Studies 201 Notes for November 19, 2003 Determining sample size for estimation of a population proportion Section 8.6.2, p. 541. As indicated in the notes for November 17, when sample size is
More information8 6 X 2 Test for a Variance or Standard Deviation
Section 8 6 x 2 Test for a Variance or Standard Deviation 437 This test uses the P-value method. Therefore, it is not necessary to enter a significance level. 1. Select MegaStat>Hypothesis Tests>Proportion
More informationIntroduction to Hypothesis Testing. Hypothesis Testing. Step 1: State the Hypotheses
Introduction to Hypothesis Testing 1 Hypothesis Testing A hypothesis test is a statistical procedure that uses sample data to evaluate a hypothesis about a population Hypothesis is stated in terms of the
More informationChapter 8 Section 1. Homework A
Chapter 8 Section 1 Homework A 8.7 Can we use the large-sample confidence interval? In each of the following circumstances state whether you would use the large-sample confidence interval. The variable
More informationCHANCE ENCOUNTERS. Making Sense of Hypothesis Tests. Howard Fincher. Learning Development Tutor. Upgrade Study Advice Service
CHANCE ENCOUNTERS Making Sense of Hypothesis Tests Howard Fincher Learning Development Tutor Upgrade Study Advice Service Oxford Brookes University Howard Fincher 2008 PREFACE This guide has a restricted
More informationIntroduction to Analysis of Variance (ANOVA) Limitations of the t-test
Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One- Way ANOVA Limitations of the t-test Although the t-test is commonly used, it has limitations Can only
More informationName: (b) Find the minimum sample size you should use in order for your estimate to be within 0.03 of p when the confidence level is 95%.
Chapter 7-8 Exam Name: Answer the questions in the spaces provided. If you run out of room, show your work on a separate paper clearly numbered and attached to this exam. Please indicate which program
More informationBivariate Statistics Session 2: Measuring Associations Chi-Square Test
Bivariate Statistics Session 2: Measuring Associations Chi-Square Test Features Of The Chi-Square Statistic The chi-square test is non-parametric. That is, it makes no assumptions about the distribution
More informationUnderstanding Confidence Intervals and Hypothesis Testing Using Excel Data Table Simulation
Understanding Confidence Intervals and Hypothesis Testing Using Excel Data Table Simulation Leslie Chandrakantha lchandra@jjay.cuny.edu Department of Mathematics & Computer Science John Jay College of
More informationSimulating Chi-Square Test Using Excel
Simulating Chi-Square Test Using Excel Leslie Chandrakantha John Jay College of Criminal Justice of CUNY Mathematics and Computer Science Department 524 West 59 th Street, New York, NY 10019 lchandra@jjay.cuny.edu
More informationTesting Hypotheses About Proportions
Chapter 11 Testing Hypotheses About Proportions Hypothesis testing method: uses data from a sample to judge whether or not a statement about a population may be true. Steps in Any Hypothesis Test 1. Determine
More informationTwo-sample hypothesis testing, II 9.07 3/16/2004
Two-sample hypothesis testing, II 9.07 3/16/004 Small sample tests for the difference between two independent means For two-sample tests of the difference in mean, things get a little confusing, here,
More informationMind on Statistics. Chapter 10
Mind on Statistics Chapter 10 Section 10.1 Questions 1 to 4: Some statistical procedures move from population to sample; some move from sample to population. For each of the following procedures, determine
More informationHypothesis Testing. Steps for a hypothesis test:
Hypothesis Testing Steps for a hypothesis test: 1. State the claim H 0 and the alternative, H a 2. Choose a significance level or use the given one. 3. Draw the sampling distribution based on the assumption
More informationMath 58. Rumbos Fall 2008 1. Solutions to Review Problems for Exam 2
Math 58. Rumbos Fall 2008 1 Solutions to Review Problems for Exam 2 1. For each of the following scenarios, determine whether the binomial distribution is the appropriate distribution for the random variable
More informationFixed-Effect Versus Random-Effects Models
CHAPTER 13 Fixed-Effect Versus Random-Effects Models Introduction Definition of a summary effect Estimating the summary effect Extreme effect size in a large study or a small study Confidence interval
More informationChapter 2. Hypothesis testing in one population
Chapter 2. Hypothesis testing in one population Contents Introduction, the null and alternative hypotheses Hypothesis testing process Type I and Type II errors, power Test statistic, level of significance
More informationIn the past, the increase in the price of gasoline could be attributed to major national or global
Chapter 7 Testing Hypotheses Chapter Learning Objectives Understanding the assumptions of statistical hypothesis testing Defining and applying the components in hypothesis testing: the research and null
More informationTwo-sample inference: Continuous data
Two-sample inference: Continuous data Patrick Breheny April 5 Patrick Breheny STA 580: Biostatistics I 1/32 Introduction Our next two lectures will deal with two-sample inference for continuous data As
More informationUnit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression
Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a
More information9 Testing the Difference
blu49076_ch09.qxd 5/1/2003 8:19 AM Page 431 c h a p t e r 9 9 Testing the Difference Between Two Means, Two Variances, and Two Proportions Outline 9 1 Introduction 9 2 Testing the Difference Between Two
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
STT315 Practice Ch 5-7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The length of time a traffic signal stays green (nicknamed
More information"Statistical methods are objective methods by which group trends are abstracted from observations on many separate individuals." 1
BASIC STATISTICAL THEORY / 3 CHAPTER ONE BASIC STATISTICAL THEORY "Statistical methods are objective methods by which group trends are abstracted from observations on many separate individuals." 1 Medicine
More informationUnit 26: Small Sample Inference for One Mean
Unit 26: Small Sample Inference for One Mean Prerequisites Students need the background on confidence intervals and significance tests covered in Units 24 and 25. Additional Topic Coverage Additional coverage
More informationA POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING
CHAPTER 5. A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING 5.1 Concepts When a number of animals or plots are exposed to a certain treatment, we usually estimate the effect of the treatment
More informationCONTINGENCY TABLES ARE NOT ALL THE SAME David C. Howell University of Vermont
CONTINGENCY TABLES ARE NOT ALL THE SAME David C. Howell University of Vermont To most people studying statistics a contingency table is a contingency table. We tend to forget, if we ever knew, that contingency
More informationAugust 2012 EXAMINATIONS Solution Part I
August 01 EXAMINATIONS Solution Part I (1) In a random sample of 600 eligible voters, the probability that less than 38% will be in favour of this policy is closest to (B) () In a large random sample,
More informationHypothesis Testing: Two Means, Paired Data, Two Proportions
Chapter 10 Hypothesis Testing: Two Means, Paired Data, Two Proportions 10.1 Hypothesis Testing: Two Population Means and Two Population Proportions 1 10.1.1 Student Learning Objectives By the end of this
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) ±1.88 B) ±1.645 C) ±1.96 D) ±2.
Ch. 6 Confidence Intervals 6.1 Confidence Intervals for the Mean (Large Samples) 1 Find a Critical Value 1) Find the critical value zc that corresponds to a 94% confidence level. A) ±1.88 B) ±1.645 C)
More informationSTATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4
STATISTICS 8, FINAL EXAM NAME: KEY Seat Number: Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 Make sure you have 8 pages. You will be provided with a table as well, as a separate
More informationHYPOTHESIS TESTING: POWER OF THE TEST
HYPOTHESIS TESTING: POWER OF THE TEST The first 6 steps of the 9-step test of hypothesis are called "the test". These steps are not dependent on the observed data values. When planning a research project,
More informationChapter 7: One-Sample Inference
Chapter 7: One-Sample Inference Now that you have all this information about descriptive statistics and probabilities, it is time to start inferential statistics. There are two branches of inferential
More informationComparing Two Groups. Standard Error of ȳ 1 ȳ 2. Setting. Two Independent Samples
Comparing Two Groups Chapter 7 describes two ways to compare two populations on the basis of independent samples: a confidence interval for the difference in population means and a hypothesis test. The
More information12.5: CHI-SQUARE GOODNESS OF FIT TESTS
125: Chi-Square Goodness of Fit Tests CD12-1 125: CHI-SQUARE GOODNESS OF FIT TESTS In this section, the χ 2 distribution is used for testing the goodness of fit of a set of data to a specific probability
More informationSample Size and Power in Clinical Trials
Sample Size and Power in Clinical Trials Version 1.0 May 011 1. Power of a Test. Factors affecting Power 3. Required Sample Size RELATED ISSUES 1. Effect Size. Test Statistics 3. Variation 4. Significance
More informationUsing Excel for inferential statistics
FACT SHEET Using Excel for inferential statistics Introduction When you collect data, you expect a certain amount of variation, just caused by chance. A wide variety of statistical tests can be applied
More informationISyE 2028 Basic Statistical Methods - Fall 2015 Bonus Project: Big Data Analytics Final Report: Time spent on social media
ISyE 2028 Basic Statistical Methods - Fall 2015 Bonus Project: Big Data Analytics Final Report: Time spent on social media Abstract: The growth of social media is astounding and part of that success was
More informationTHE FIRST SET OF EXAMPLES USE SUMMARY DATA... EXAMPLE 7.2, PAGE 227 DESCRIBES A PROBLEM AND A HYPOTHESIS TEST IS PERFORMED IN EXAMPLE 7.
THERE ARE TWO WAYS TO DO HYPOTHESIS TESTING WITH STATCRUNCH: WITH SUMMARY DATA (AS IN EXAMPLE 7.17, PAGE 236, IN ROSNER); WITH THE ORIGINAL DATA (AS IN EXAMPLE 8.5, PAGE 301 IN ROSNER THAT USES DATA FROM
More informationThe Math. P (x) = 5! = 1 2 3 4 5 = 120.
The Math Suppose there are n experiments, and the probability that someone gets the right answer on any given experiment is p. So in the first example above, n = 5 and p = 0.2. Let X be the number of correct
More informationChapter 7 Review. Confidence Intervals. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Chapter 7 Review Confidence Intervals MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Suppose that you wish to obtain a confidence interval for
More informationUsing Stata for Categorical Data Analysis
Using Stata for Categorical Data Analysis NOTE: These problems make extensive use of Nick Cox s tab_chi, which is actually a collection of routines, and Adrian Mander s ipf command. From within Stata,
More informationUnit 27: Comparing Two Means
Unit 27: Comparing Two Means Prerequisites Students should have experience with one-sample t-procedures before they begin this unit. That material is covered in Unit 26, Small Sample Inference for One
More informationHYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...
HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men
More informationIndependent t- Test (Comparing Two Means)
Independent t- Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent t-test when to use the independent t-test the use of SPSS to complete an independent
More informationUNDERSTANDING THE INDEPENDENT-SAMPLES t TEST
UNDERSTANDING The independent-samples t test evaluates the difference between the means of two independent or unrelated groups. That is, we evaluate whether the means for two independent groups are significantly
More informationStatistics 100A Homework 4 Solutions
Chapter 4 Statistics 00A Homework 4 Solutions Ryan Rosario 39. A ball is drawn from an urn containing 3 white and 3 black balls. After the ball is drawn, it is then replaced and another ball is drawn.
More informationElementary Statistics
lementary Statistics Chap10 Dr. Ghamsary Page 1 lementary Statistics M. Ghamsary, Ph.D. Chapter 10 Chi-square Test for Goodness of fit and Contingency tables lementary Statistics Chap10 Dr. Ghamsary Page
More informationPractice Midterm Exam #2
The Islamic University of Gaza Faculty of Engineering Department of Civil Engineering 12/12/2009 Statistics and Probability for Engineering Applications 9.2 X is a binomial random variable, show that (
More informationLAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING
LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.
More informationClass 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
More information6: Introduction to Hypothesis Testing
6: Introduction to Hypothesis Testing Significance testing is used to help make a judgment about a claim by addressing the question, Can the observed difference be attributed to chance? We break up significance
More informationStat 411/511 THE RANDOMIZATION TEST. Charlotte Wickham. stat511.cwick.co.nz. Oct 16 2015
Stat 411/511 THE RANDOMIZATION TEST Oct 16 2015 Charlotte Wickham stat511.cwick.co.nz Today Review randomization model Conduct randomization test What about CIs? Using a t-distribution as an approximation
More informationChapter Four. Data Analyses and Presentation of the Findings
Chapter Four Data Analyses and Presentation of the Findings The fourth chapter represents the focal point of the research report. Previous chapters of the report have laid the groundwork for the project.
More information1 Hypothesis Testing. H 0 : population parameter = hypothesized value:
1 Hypothesis Testing In Statistics, a hypothesis proposes a model for the world. Then we look at the data. If the data are consistent with that model, we have no reason to disbelieve the hypothesis. Data
More informationChapter 7 Section 7.1: Inference for the Mean of a Population
Chapter 7 Section 7.1: Inference for the Mean of a Population Now let s look at a similar situation Take an SRS of size n Normal Population : N(, ). Both and are unknown parameters. Unlike what we used
More informationStatistiek I. Proportions aka Sign Tests. John Nerbonne. CLCG, Rijksuniversiteit Groningen. http://www.let.rug.nl/nerbonne/teach/statistiek-i/
Statistiek I Proportions aka Sign Tests John Nerbonne CLCG, Rijksuniversiteit Groningen http://www.let.rug.nl/nerbonne/teach/statistiek-i/ John Nerbonne 1/34 Proportions aka Sign Test The relative frequency
More informationUniversity of Chicago Graduate School of Business. Business 41000: Business Statistics
Name: University of Chicago Graduate School of Business Business 41000: Business Statistics Special Notes: 1. This is a closed-book exam. You may use an 8 11 piece of paper for the formulas. 2. Throughout
More information