9.1 Basic Principles of Hypothesis Testing


 Silvia Cooper
 2 years ago
 Views:
Transcription
1 9. Basic Principles of Hypothesis Testing Basic Idea Through an Example: On the very first day of class I gave the example of tossing a coin times, and what you might conclude about the fairness of the coin depending on the outcome of this experiment. If you got 55 heads, would you conclude that the coin was not fair? What if you got 95 heads? What if you got 75 heads? The further away our sample is from the expected value, the more suspicious we would be that the coin is not fair. Now having some knowledge about probabilities, you could find out how unlikely it is to get 75 heads or more out of if in fact the coin was fair (the probability is zero). So in a case like that, we could conclude that the coin must not be fair. In chapter 9 we will use hypothesis testing to make decisions about a population parameter ( µ or p ) based on the value of a sample statistics. The idea behind hypothesis testing is the same as the idea behind a criminal trial. The person is presumed to be not guilty until there is sufficient evidence to declare the person guilty. A null hypothesis, denoted H, states that some parameter is equal to a specific value, ex. H : µ = 27 (always use an equal sign for H ). The null hypothesis is a claim about a population parameter that is assumed to be true until declared false. An alternative hypothesis, denoted H, states that the value of the parameter differs from that specified by the null hypothesis, ex. H : µ 27 (a twotailed test), or H : 27 µ > (a righttailed test), or H : 27 µ < (a lefttailed test). The alternative hypothesis is a claim about a population parameter that will be true if the null hypothesis is false. Examples: Null hypothesis: H : The coin is fair (.5 Alternative hypothesis: H : The coin is not fair ( p.5 or p.5 or p.5 Null hypothesis: H : The person is not guilty Alternative hypothesis: H : The person is guilty Consider the M&M experiment that we did in class. What were the hypotheses? Null hypothesis: Alternative hypothesis:
2 Conclusions We reject H if the value of our test statistics falls too far away from the assumed population parameter. This is the same as saying that we support the H claim. We usually write this conclusion as "There is sufficient evidence to show that... H... ", where H is stated in words. We fail to reject H, if the difference between the sample statistics and the assumed population parameter is small, since the difference may be due to chance. We usually write this conclusion as "There is not sufficient evidence to show that... H... ", where H is stated in words. Note how we don't say that H is true. But we could say that " H may be true". Errors Our conclusion will be to either reject the null hypothesis or fail to reject it. Such conclusions are sometimes correct and sometimes not. There are two types of errors: Type I error occurs when rejecting the null hypothesis when it is actually true. The probability of making a type I error is α, the significance level. ex. Person is found guilty in court even though he did not commit the crime ex. Coin was found to be unfair even though it is fair. Type II error occurs when failing to reject the null hypothesis, when it is actually false. The probability of making a type II error is β (beta). ex. Person is found not guilty in court even though he did commit the crime. ex. Coin was found to be fair even though it is unfair. Fill each cell in the table with one of the following: Type I Error, Type II Error, or Correct Decision. Decision Reject H The Truth H is true H is false Do not reject H
3 . Test if the mean weight of women who won Miss America titles is still equal to 2 lb, or if it has changed. State hypotheses: Is it a lefttailed, righttailed, or twotailed test? If the null hypothesis is rejected, state an appropriate conclusion: What kind of error could we have made? 2. Plain M&M candies supposedly haves a mean weight that is.8535g. Test if the candies' weight is less than that. State hypotheses: Is it a lefttailed, righttailed, or twotailed test? If the null hypothesis is not rejected, state an appropriate conclusion: What kind of error could we have made? 3. Test if more than 25% of Internet users pay bills online. State hypotheses: Is it a lefttailed, righttailed, or twotailed test? If the null hypothesis is not rejected, state an appropriate conclusion: What kind of error could we have made? 4. Test if the mean hours spent per week on house chores by all housewives is less than 3. State hypotheses: Is it a lefttailed, righttailed, or twotailed test? If the null hypothesis is rejected, state an appropriate conclusion: What kind of error could we have made?
4 9.2  Hypothesis Tests About µ when σ is Known The Test Statistic is a value used in making a decision about the null hypothesis, and it is found by converting 2 the sample statistic ( x, ˆp, or s) to a score (such as z, t, or χ ) with the assumption that the null hypothesis is true. The probability that we use to determine whether an event is unusual is called the significance level of the test, and is denoted by α. If we reject H after choosing a significance level α, we say that the result is statistically significant at the α level (note that statistically significant doesn't always mean practically significant). We also say that H is rejected at the α level. The Pvalue is the probability of getting a value of the test statistic that is at least as extreme as the one representing the sample data, assuming that the null hypothesis is true. "At least as extreme" means " as far away from the expected parameter as we got, or even further". If the Pvalue is very small, it means that the probability of getting what we got in our sample is very small, which may indicate that our original assumption H is not true. H is rejected if the Pvalue is smaller than the significance level α. In a left tailed test: Pvalue = area to the left of the test statistic Pvalue Test Stat In a right tailed test: Pvalue = area to the right of the test statistic Pvalue In a two tailed test: Pvalue = twice the area in the tail beyond the test statistic Pvalue / 2 Test Stat Pvalue is the total area of both tails Pvalue / 2 Test Stat or Test Stat
5 Hypothesis Tests About µ when σ is Known: Requirements. The value of the population standard deviation σ is known. 2. Either or both of these conditions is satisfied: The population is normally distributed or n > 3. If above is satisfied we know that the sampling distribution of x is Normal. Test Statistics: x µ z = where σ x = σ x σ n 8Step Procedure for Performing a Hypothesis Test: ) State the null and alternative hypotheses of the test. 2) Choose and/or state the significance levelα. 3) State type of test, the standardized sampling distribution that should be used, and check that all of the required assumptions for using that distribution are satisfied. 4) Compute the test statistic. 5) Draw a picture of the standardized sampling distribution you are using. Label the test statistic. 6) Calculate the Pvalue. 7) Interpret the Pvalue and make a decision. If Pvalue < α then we reject the null hypothesis, and we have sufficient evidence for the alternative hypothesis. If Pvalue > α then we do NOT reject the null hypothesis, and we do NOT have sufficient evidence for the alternative hypothesis. 8) State a conclusion in the form of a detailed sentence that addresses the alternative hypothesis. When we Reject H, we say there is sufficient evidence to show that H, where H is stated in words. When we Fail to Reject H, we say there is not sufficient evidence to show that H, where H is stated in words.
6 When presenting the results of a hypothesis test, one should report the Pvalue or the value of the test statistics. That way the reader can tell exactly how likely or unlikely the test statistics was, and he/she can determine whether H could be rejected at a different level. Relationship between hypothesis tests and confidence intervals: If we test H : µ = µ vs. H: µ µ, then if the (α )% confidence interval contains µ, then H will not be rejected at the α level if the (α )% confidence interval does not contain µ, then H will be rejected at the α level P(type I error) = α and P(type II error) = β The smaller the probability of a type I error becomes, the larger the probability of a type II error becomes. Examples:. (a) The print on the package of watt General Electric softwhite lightbulbs says that these bulbs have an average life of 75 hours. Assume that the lives of all such bulbs have a normal distribution with a standard deviation of 55 hours. The mean life of a simple random sample of 25 such bulbs was 725 hours. We are concerned that the stated average life on the package is exaggerated. Test at 5% significance level if this is true. (b) Would your conclusion be different if the significance level was %?
7 2. A certain type of children's pain reliever states that it contains 325 mg of acetaminophen in each ounce of the drug. If 7 one ounce samples are tested for acetaminophen and it is determined that the sample mean is 39 mg of the drug and a population standard deviation of 26 mg. With a =., test the claim that the population mean is equal to 325 mg. We can check our answers by using programs in our calculators. Press STAT and go to TESTS
8 3. A random sample of 6 secondgraders in a certain school district are given a standardized mathematics skills test. The sample mean score is 52. Assume the standard deviation of test scores is 5. The nationwide average score on this test is 5.The school superintendent wants to know whether the secondgraders in her school district have greater math skills than the nationwide average. Use a. level of significance to test this. We never accept the null hypothesis Note, that if we Fail to Reject H, we never say we accept H because the sample data is evidence against H (in favor of H ). It is not evidence in favor of H. We cannot prove something is true when we had to assume it was true to get the test started. ex. In the famous O.J. Simpson trial there was not sufficient evidence to show that O.J. Simpson was guilty of murder. That does not mean he was innocent.
9 4. When 4 people used the Atkins diet for one year, their mean weight change was 2. lb (new weight  old weight). Assume that the standard deviation of all such weight changes is σ =4.8 lb and use a.5 significance level to test the claim that the mean weight change is less than. Based on the results, does the diet appear to be effective? Does the mean weight change appear to be substantial enough to justify the special diet?
10 9.3  Hypothesis Tests About µ when σ is Not Known Requirements. The value of the population standard deviation σ is NOT known. 2. Either or both of these conditions are satisfied: The population is normally distributed or n > 3. If above is satisfied we know that the sampling distribution of x is Normal. x µ Test Statistics: t = where sx s x = s n The 8step procedure for performing a hypothesis test:. State the null and alternative hypotheses. 2. State significance level α 3. State which test to use and why. 4. Calculate the test statistic. 5. Draw a picture and label the test statistic. 6. Calculate the pvalue. 7. Interpret pvalue and make a decision. 8. State your conclusion.. A softdrink manufacturer claims that its 2ounce cans do not contain, on average, more than 3 calories. A random sample of 64 cans of this soft drink, which were checked for calories, contained a mean of 32 calories with a standard deviation of 3 calories. Does the sample information support the alternative hypothesis that the manufacturer's claim is false? Use a significance level of 5%.
11 2. The insurance Institute for Highway Safety conducted tests with crashes of new cars traveling at 6mi/h. Total cost of the damage was found. Results are listed below for a simple random sample of the tested cars. Assume the population has a distribution that is approximately normal. $7448 $49 $95 $6374 $4277 Use a. significance level to test the claim that when tested under the same conditions, the damage costs for the population of cars have a mean of $5. 3. A simple random sample of 4 recorded speeds (in mph) is obtained from cars traveling on a section of Highway 45 in Los Angeles. The sample has a mean of 68.4 mph and a standard deviation of 5.7 mph. Use a.5 significance level to test the claim that the mean speed of all cars is greater than the posted speed limit of 65 mph.
12 9.4  Hypothesis Tests About a Population Proportion Requirements. We have a simple random sample 2. The population is at least 2 times as large as the sample. 3. The items in the population are divided into two categories. 4. The sample must contain at least individuals in each category. If above is satisfied we know that the sampling distribution of ˆp is approximately Normal. pˆ p p ( p) Test Statistics: z = where σ pˆ = σ n pˆ The 8step procedure for performing a hypothesis test:. State the null and alternative hypotheses. 2. State significance level α 3. State which test to use and why. 4. Calculate the test statistic. 5. Draw a picture and label the test statistic. 6. Calculate the pvalue. 7. Interpret pvalue and make a decision. 8. State your conclusion.. Trials in an experiment with a polygraph (lie detector) has 98 results that include 24 cases of wrong results and 74 cases of correct results. Use a.5 significance level to test the claim that such polygraph results are correct less than 8% of the time. Based on the results, should polygraph test results be prohibited as evidence in trials?
13 2. (a) 9yearold Emily Rosa chose the topic of touch therapy for a science fair project. She convinced 2 experienced touch therapists to participate in a simple test of their ability to detect human energy field. Emily constructed a cardboard partition with two holes for hands. Each touch therapist would put both hands through the two holes, and Emily would place her hand just above one of the therapist's hands and ask the therapist to identify the hand that Emily had selected. Emily used a coin toss to randomly select which hand to use. This test was repeated 28 times. If the touch therapists really did have the ability to sense a human energy field, they should have identified the correct hand much more than 5% of the time. If they just guessed, they should have been correct about 5% of the time. The touch therapists identified the correct hand 23 times out of the total 28 times, which is a success rate of 44%. Use a.5 significance level to test the claim that touch therapists are correct less than 5% of the time. (b) Would a different significance level change your conclusion in part (a)? (c) Can you argue against the validity of this study?
Chapter 8. Hypothesis Testing
Chapter 8 Hypothesis Testing Hypothesis In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing
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 information82 Basics of Hypothesis Testing. Definitions. Rare Event Rule for Inferential Statistics. Null Hypothesis
82 Basics of Hypothesis Testing Definitions This section presents individual components of a hypothesis test. We should know and understand the following: How to identify the null hypothesis and alternative
More informationChapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 81 Overview 82 Basics of Hypothesis Testing
Chapter 8 Hypothesis Testing 1 Chapter 8 Hypothesis Testing 81 Overview 82 Basics of Hypothesis Testing 83 Testing a Claim About a Proportion 85 Testing a Claim About a Mean: s Not Known 86 Testing
More informationMATH 10: Elementary Statistics and Probability Chapter 9: Hypothesis Testing with One Sample
MATH 10: Elementary Statistics and Probability Chapter 9: Hypothesis Testing with One Sample Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of
More informationExample Hypotheses. Chapter 82: Basics of Hypothesis Testing. A newspaper headline makes the claim: Most workers get their jobs through networking
Chapter 82: Basics of Hypothesis Testing Two main activities in statistical inference are using sample data to: 1. estimate a population parameter forming confidence intervals 2. test a hypothesis or
More informationChapter III. Testing Hypotheses
Chapter III Testing Hypotheses R (Introduction) A statistical hypothesis is an assumption about a population parameter This assumption may or may not be true The best way to determine whether a statistical
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 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 informationNull Hypothesis H 0. The null hypothesis (denoted by H 0
Hypothesis test In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing a claim about a property
More informationChapter 8 Introduction to Hypothesis Testing
Chapter 8 Student Lecture Notes 81 Chapter 8 Introduction to Hypothesis Testing Fall 26 Fundamentals of Business Statistics 1 Chapter Goals After completing this chapter, you should be able to: Formulate
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 informationA Trial Analogy for Statistical. Hypothesis Testing. Legal Trial Begin with claim: Statistical Significance Test Hypotheses (statements)
A Trial Analogy for Statistical Slide 1 Hypothesis Testing Legal Trial Begin with claim: Smith is not guilty If this is rejected, we accept Smith is guilty reasonable doubt Present evidence (facts) Evaluate
More information22. HYPOTHESIS TESTING
22. HYPOTHESIS TESTING Often, we need to make decisions based on incomplete information. Do the data support some belief ( hypothesis ) about the value of a population parameter? Is OJ Simpson guilty?
More informationChapter Additional: Standard Deviation and Chi Square
Chapter Additional: Standard Deviation and Chi Square Chapter Outline: 6.4 Confidence Intervals for the Standard Deviation 7.5 Hypothesis testing for Standard Deviation Section 6.4 Objectives Interpret
More informationHypothesis testing allows us to use a sample to decide between two statements made about a Population characteristic.
Hypothesis Testing Hypothesis testing allows us to use a sample to decide between two statements made about a Population characteristic. Population Characteristics are things like The mean of a population
More informationHypothesis Testing. Concept of Hypothesis Testing
Quantitative Methods 2013 Hypothesis Testing with One Sample 1 Concept of Hypothesis Testing Testing Hypotheses is another way to deal with the problem of making a statement about an unknown population
More informationChapter 7 Part 2. Hypothesis testing Power
Chapter 7 Part 2 Hypothesis testing Power November 6, 2008 All of the normal curves in this handout are sampling distributions Goal: To understand the process of hypothesis testing and the relationship
More informationLecture 8 Hypothesis Testing
Lecture 8 Hypothesis Testing Fall 2013 Prof. Yao Xie, yao.xie@isye.gatech.edu H. Milton Stewart School of Industrial Systems & Engineering Georgia Tech Midterm 1 Score 46 students Highest score: 98 Lowest
More informationStep 1: Set up hypotheses that ask a question about the population by setting up two opposite statements about the possible value of the parameters.
HYPOTHESIS TEST CLASS NOTES Hypothesis Test: Procedure that allows us to ask a question about an unknown population parameter Uses sample data to draw a conclusion about the unknown population parameter.
More informationSection 12.2, Lesson 3. What Can Go Wrong in Hypothesis Testing: The Two Types of Errors and Their Probabilities
Today: Section 2.2, Lesson 3: What can go wrong with hypothesis testing Section 2.4: Hypothesis tests for difference in two proportions ANNOUNCEMENTS: No discussion today. Check your grades on eee and
More informationCh. 8 Hypothesis Testing
Ch. 8 Hypothesis Testing 8.1 Foundations of Hypothesis Testing Definitions In statistics, a hypothesis is a claim about a property of a population. A hypothesis test is a standard procedure for testing
More informationSampling and Hypothesis Testing
Population and sample Sampling and Hypothesis Testing Allin Cottrell Population : an entire set of objects or units of observation of one sort or another. Sample : subset of a population. Parameter versus
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 informationChapter 7. Hypothesis Testing with One Sample
Chapter 7 Hypothesis Testing with One Sample 7.1 Introduction to Hypothesis Testing Hypothesis Tests A hypothesis test is a process that uses sample statistics to test a claim about the value of a population
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 informationHow to Conduct a Hypothesis Test
How to Conduct a Hypothesis Test The idea of hypothesis testing is relatively straightforward. In various studies we observe certain events. We must ask, is the event due to chance alone, or is there some
More informationHypoTesting. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Class: Date: HypoTesting Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A Type II error is committed if we make: a. a correct decision when the
More informationChapter 9, Part A Hypothesis Tests. Learning objectives
Chapter 9, Part A Hypothesis Tests Slide 1 Learning objectives 1. Understand how to develop Null and Alternative Hypotheses 2. Understand Type I and Type II Errors 3. Able to do hypothesis test about population
More informationLecture 13 More on hypothesis testing
Lecture 13 More on hypothesis testing Thais Paiva STA 111  Summer 2013 Term II July 22, 2013 1 / 27 Thais Paiva STA 111  Summer 2013 Term II Lecture 13, 07/22/2013 Lecture Plan 1 Type I and type II error
More informationConfidence Interval: pˆ = E = Indicated decision: < p <
Hypothesis (Significance) Tests About a Proportion Example 1 The standard treatment for a disease works in 0.675 of all patients. A new treatment is proposed. Is it better? (The scientists who created
More informationPROBLEM SET 1. For the first three answer true or false and explain your answer. A picture is often helpful.
PROBLEM SET 1 For the first three answer true or false and explain your answer. A picture is often helpful. 1. Suppose the significance level of a hypothesis test is α=0.05. If the pvalue of the test
More informationHypothesis Testing I
ypothesis Testing I The testing process:. Assumption about population(s) parameter(s) is made, called null hypothesis, denoted. 2. Then the alternative is chosen (often just a negation of the null hypothesis),
More informationHomework #3 is due Friday by 5pm. Homework #4 will be posted to the class website later this week. It will be due Friday, March 7 th, at 5pm.
Homework #3 is due Friday by 5pm. Homework #4 will be posted to the class website later this week. It will be due Friday, March 7 th, at 5pm. Political Science 15 Lecture 12: Hypothesis Testing Sampling
More informationChapter 7. Section Introduction to Hypothesis Testing
Section 7.1  Introduction to Hypothesis Testing Chapter 7 Objectives: State a null hypothesis and an alternative hypothesis Identify type I and type II errors and interpret the level of significance Determine
More informationHYPOTHESIS TESTING: POWER OF THE TEST
HYPOTHESIS TESTING: POWER OF THE TEST The first 6 steps of the 9step test of hypothesis are called "the test". These steps are not dependent on the observed data values. When planning a research project,
More informationStatistical inference provides methods for drawing conclusions about a population from sample data.
Chapter 15 Tests of Significance: The Basics Statistical inference provides methods for drawing conclusions about a population from sample data. Two of the most common types of statistical inference: 1)
More information15.0 More Hypothesis Testing
15.0 More Hypothesis Testing 1 Answer Questions Type I and Type II Error Power Calculation Bayesian Hypothesis Testing 15.1 Type I and Type II Error In the philosophy of hypothesis testing, the null hypothesis
More informationChapter 8. Professor Tim Busken. April 20, Chapter 8. Tim Busken. 8.2 Basics of. Hypothesis Testing. Works Cited
Chapter 8 Professor April 20, 2014 In Chapter 8, we continue our study of inferential statistics. Concept: Inferential Statistics The two major activities of inferential statistics are 1 to use sample
More informationHypothesis Testing: pvalue
STAT 101 Dr. Kari Lock Morgan Paul the Octopus Hypothesis Testing: SECTION 4.2 andomization distribution http://www.youtube.com/watch?v=3esgpumj9e Hypotheses In 2008, Paul the Octopus predicted 8 World
More informationThe alternative hypothesis,, is the statement that the parameter value somehow differs from that claimed by the null hypothesis. : 0.5 :>0.5 :<0.
Section 8.28.5 Null and Alternative Hypotheses... The null hypothesis,, is a statement that the value of a population parameter is equal to some claimed value. :=0.5 The alternative hypothesis,, is the
More informationHypothesis testing. c 2014, Jeffrey S. Simonoff 1
Hypothesis testing So far, we ve talked about inference from the point of estimation. We ve tried to answer questions like What is a good estimate for a typical value? or How much variability is there
More informationModule 7: Hypothesis Testing I Statistics (OA3102)
Module 7: Hypothesis Testing I Statistics (OA3102) Professor Ron Fricker Naval Postgraduate School Monterey, California Reading assignment: WM&S chapter 10.110.5 Revision: 212 1 Goals for this Module
More informationHypothesis testing: Examples. AMS7, Spring 2012
Hypothesis testing: Examples AMS7, Spring 2012 Example 1: Testing a Claim about a Proportion Sect. 7.3, # 2: Survey of Drinking: In a Gallup survey, 1087 randomly selected adults were asked whether they
More informationModule 5 Hypotheses Tests: Comparing Two Groups
Module 5 Hypotheses Tests: Comparing Two Groups Objective: In medical research, we often compare the outcomes between two groups of patients, namely exposed and unexposed groups. At the completion of this
More informationHomework 5 Solutions
Math 130 Assignment Chapter 18: 6, 10, 38 Chapter 19: 4, 6, 8, 10, 14, 16, 40 Chapter 20: 2, 4, 9 Chapter 18 Homework 5 Solutions 18.6] M&M s. The candy company claims that 10% of the M&M s it produces
More informationHypothesis testing for µ:
University of California, Los Angeles Department of Statistics Statistics 13 Elements of a hypothesis test: Hypothesis testing Instructor: Nicolas Christou 1. Null hypothesis, H 0 (always =). 2. Alternative
More informationCHAPTER 11 SECTION 2: INTRODUCTION TO HYPOTHESIS TESTING
CHAPTER 11 SECTION 2: INTRODUCTION TO HYPOTHESIS TESTING MULTIPLE CHOICE 56. In testing the hypotheses H 0 : µ = 50 vs. H 1 : µ 50, the following information is known: n = 64, = 53.5, and σ = 10. The standardized
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 78 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 informationreductio ad absurdum null hypothesis, alternate hypothesis
Chapter 10 s Using a Single Sample 10.1: Hypotheses & Test Procedures Basics: In statistics, a hypothesis is a statement about a population characteristic. s are based on an reductio ad absurdum form of
More informationWording of Final Conclusion. Slide 1
Wording of Final Conclusion Slide 1 8.3: Assumptions for Testing Slide 2 Claims About Population Means 1) The sample is a simple random sample. 2) The value of the population standard deviation σ is known
More informationCorrelational Research
Correlational Research Chapter Fifteen Correlational Research Chapter Fifteen Bring folder of readings The Nature of Correlational Research Correlational Research is also known as Associational Research.
More informationChapter 21. More About Tests and Intervals. Copyright 2012, 2008, 2005 Pearson Education, Inc.
Chapter 21 More About Tests and Intervals Copyright 2012, 2008, 2005 Pearson Education, Inc. Zero In on the Null Null hypotheses have special requirements. To perform a hypothesis test, the null must be
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 informationBA 275 Review Problems  Week 6 (10/30/0611/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394398, 404408, 410420
BA 275 Review Problems  Week 6 (10/30/0611/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394398, 404408, 410420 1. Which of the following will increase the value of the power in a statistical test
More informationBasic Statistics Self Assessment Test
Basic Statistics Self Assessment Test Professor Douglas H. Jones PAGE 1 A sodadispensing machine fills 12ounce cans of soda using a normal distribution with a mean of 12.1 ounces and a standard deviation
More information4) The role of the sample mean in a confidence interval estimate for the population mean is to: 4)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Assume that the change in daily closing prices for stocks on the New York Stock Exchange is a random
More informationChapter 1 Hypothesis Testing
Chapter 1 Hypothesis Testing Principles of Hypothesis Testing tests for one sample case 1 Statistical Hypotheses They are defined as assertion or conjecture about the parameter or parameters of a population,
More informationReasoning with Uncertainty More about Hypothesis Testing. Pvalues, types of errors, power of a test
Reasoning with Uncertainty More about Hypothesis Testing Pvalues, types of errors, power of a test PValues and Decisions Your conclusion about any null hypothesis should be accompanied by the Pvalue
More informationHypothesis Testing with One Sample. Introduction to Hypothesis Testing 7.1. Hypothesis Tests. Chapter 7
Chapter 7 Hypothesis Testing with One Sample 71 Introduction to Hypothesis Testing Hypothesis Tests A hypothesis test is a process that uses sample statistics to test a claim about the value of a population
More informationHypothesis testing  Steps
Hypothesis testing  Steps Steps to do a twotailed test of the hypothesis that β 1 0: 1. Set up the hypotheses: H 0 : β 1 = 0 H a : β 1 0. 2. Compute the test statistic: t = b 1 0 Std. error of b 1 =
More informationChapter 08. Introduction
Chapter 08 Introduction Hypothesis testing may best be summarized as a decision making process in which one attempts to arrive at a particular conclusion based upon "statistical" evidence. A typical hypothesis
More informationProbability, Binomial Distributions and Hypothesis Testing Vartanian, SW 540
Probability, Binomial Distributions and Hypothesis Testing Vartanian, SW 540 1. Assume you are tossing a coin 11 times. The following distribution gives the likelihoods of getting a particular number of
More informationThe GoodnessofFit Test
on the Lecture 49 Section 14.3 HampdenSydney College Tue, Apr 21, 2009 Outline 1 on the 2 3 on the 4 5 Hypotheses on the (Steps 1 and 2) (1) H 0 : H 1 : H 0 is false. (2) α = 0.05. p 1 = 0.24 p 2 = 0.20
More information81 82 83 84 85 86
81 Review and Preview 82 Basics of Hypothesis Testing 83 Testing a Claim About a Proportion 84 Testing a Claim About a Mean: s Known 85 Testing a Claim About a Mean: s Not Known 86 Testing a Claim
More informationChapter 8 Hypothesis Testing
Chapter 8 Hypothesis Testing Chapter problem: Does the MicroSort method of gender selection increase the likelihood that a baby will be girl? MicroSort: a genderselection method developed by Genetics
More informationHypothesis Tests for a Population Proportion
Hypothesis Tests for a Population Proportion MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2015 Review: Steps of Hypothesis Testing 1. A statement is made regarding
More informationExtending Hypothesis Testing. pvalues & confidence intervals
Extending Hypothesis Testing pvalues & confidence intervals So far: how to state a question in the form of two hypotheses (null and alternative), how to assess the data, how to answer the question by
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 informationOnline 12  Sections 9.1 and 9.2Doug Ensley
Student: Date: Instructor: Doug Ensley Course: MAT117 01 Applied Statistics  Ensley Assignment: Online 12  Sections 9.1 and 9.2 1. Does a Pvalue of 0.001 give strong evidence or not especially strong
More informationHypothesis Testing  II
3σ 2σ +σ +2σ +3σ Hypothesis Testing  II Lecture 9 0909.400.01 / 0909.400.02 Dr. P. s Clinic Consultant Module in Probability & Statistics in Engineering Today in P&S 3σ 2σ +σ +2σ +3σ Review: Hypothesis
More informationThird Midterm Exam (MATH1070 Spring 2012)
Third Midterm Exam (MATH1070 Spring 2012) Instructions: This is a one hour exam. You can use a notesheet. Calculators are allowed, but other electronics are prohibited. 1. [40pts] Multiple Choice Problems
More informationTesting: is my coin fair?
Testing: is my coin fair? Formally: we want to make some inference about P(head) Try it: toss coin several times (say 7 times) Assume that it is fair ( P(head)= ), and see if this assumption is compatible
More informationNotes 8: Hypothesis Testing
Notes 8: Hypothesis Testing Julio Garín Department of Economics Statistics for Economics Spring 2012 (Stats for Econ) Hypothesis Testing Spring 2012 1 / 44 Introduction Why we conduct surveys? We want
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 informationPurpose of Hypothesis Testing
Large sample Tests of Hypotheses Chapter 9 1 Purpose of Hypothesis Testing In the last chapter, we studied methods of estimating a parameter (μ, p or p 1 p 2 ) based on sample data: point estimation confidence
More informationBusiness Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing
Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing 1) Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures
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 informationThe Basics of a Hypothesis Test
Overview The Basics of a Test Dr Tom Ilvento Department of Food and Resource Economics Alternative way to make inferences from a sample to the Population is via a Test A hypothesis test is based upon A
More informationConfidence Intervals (Review)
Intro to Hypothesis Tests Solutions STATUB.0103 Statistics for Business Control and Regression Models Confidence Intervals (Review) 1. Each year, construction contractors and equipment distributors from
More informationHomework 6 Solutions
Math 17, Section 2 Spring 2011 Assignment Chapter 20: 12, 14, 20, 24, 34 Chapter 21: 2, 8, 14, 16, 18 Chapter 20 20.12] Got Milk? The student made a number of mistakes here: Homework 6 Solutions 1. Null
More informationIntroduction to. Hypothesis Testing CHAPTER LEARNING OBJECTIVES. 1 Identify the four steps of hypothesis testing.
Introduction to Hypothesis Testing CHAPTER 8 LEARNING OBJECTIVES After reading this chapter, you should be able to: 1 Identify the four steps of hypothesis testing. 2 Define null hypothesis, alternative
More informationHypothesis Testing: General Framework 1 1
Hypothesis Testing: General Framework Lecture 2 K. Zuev February 22, 26 In previous lectures we learned how to estimate parameters in parametric and nonparametric settings. Quite often, however, researchers
More informationChapter Five: Paired Samples Methods 1/38
Chapter Five: Paired Samples Methods 1/38 5.1 Introduction 2/38 Introduction Paired data arise with some frequency in a variety of research contexts. Patients might have a particular type of laser surgery
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 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 informationThe Purpose of Hypothesis Testing
Section 8 1A: An Introduction to Hypothesis Testing The Purpose of Hypothesis Testing Seeʼs Candy states that a box of itʼs candy weighs 16 oz. They do not mean that every single box weights exactly 16
More informationAn Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10 TWOSAMPLE 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 TWOSAMPLE TESTS Practice
More information7 Hypothesis testing  one sample tests
7 Hypothesis testing  one sample tests 7.1 Introduction Definition 7.1 A hypothesis is a statement about a population parameter. Example A hypothesis might be that the mean age of students taking MAS113X
More informationHypothesis Testing. Bluman Chapter 8
CHAPTER 8 Learning Objectives C H A P T E R E I G H T Hypothesis Testing 1 Outline 81 Steps in Traditional Method 82 z Test for a Mean 83 t Test for a Mean 84 z Test for a Proportion 85 2 Test for
More informationCalculating PValues. Parkland College. Isela Guerra Parkland College. Recommended Citation
Parkland College A with Honors Projects Honors Program 2014 Calculating PValues Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating PValues" (2014). A with Honors Projects.
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 informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
STA2023 Module 10 Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A hypothesis test is to be performed. Determine the null and alternative
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 informationIQ of deaf children example: Are the deaf children lower in IQ? Or are they average? If µ100 and σ 2 225, is the 88.07 from the sample of N59 deaf chi
PSY 511: Advanced Statistics for Psychological and Behavioral Research 1 All inferential statistics have the following in common: Use of some descriptive statistic Use of probability Potential for estimation
More informationIntroduction to Hypothesis Testing. Point estimation and confidence intervals are useful statistical inference procedures.
Introduction to Hypothesis Testing Point estimation and confidence intervals are useful statistical inference procedures. Another type of inference is used frequently used concerns tests of hypotheses.
More informationNUMB3RS Activity: Candy Pieces. Episode: End of Watch
Teacher Page 1 NUMB3RS Activity: Candy Pieces Topic: Chisquare test for goodnessoffit Grade Level: 1112 Objective: Use a chisquare test to determine if there is a significant difference between the
More informationSingle sample hypothesis testing, II 9.07 3/02/2004
Single sample hypothesis testing, II 9.07 3/02/2004 Outline Very brief review Onetailed vs. twotailed tests Small sample testing Significance & multiple tests II: Data snooping What do our results mean?
More informationProbability & Statistics
Probability & Statistics BITS Pilani K K Birla Goa Campus Dr. Jajati Keshari Sahoo Department of Mathematics TEST OF HYPOTHESIS There are many problems in which, rather then estimating the value of a parameter,
More informationAP Statistics Hypothesis Testing Chapter 9. Intro to Significance Tests
Intro to Significance Tests Name Hr For the following pairs, indicate whether they are legitimate hypotheses and why. 1. 2. 3. 4. For each situation, state the null and alternate hypothesis. (Define your
More information