Hypothesis Testing (unknown σ)

Save this PDF as:

Size: px
Start display at page:

Transcription

1 Hypothesis Testing (unknown σ) Business Statistics Recall: Plan for Today Null and Alternative Hypotheses Types of errors: type I, type II Types of correct decisions: type A, type B Level of Significance and Power of the Test Hypothesis testing with unknown σ Examples 1

2 Null and Alternative hypothesis Hypothesis : A statement about the value of a population parameter. In case of two hypotheses, the statement assumed to be true is called the null hypothesis (notation H0) and the contradictory statement is called the alternative hypothesis (notation Ha). Hypothesis testing : Based on sample evidence, a procedure for determining whether the hypothesis stated is a reasonable statement and should not be rejected, or is unreasonable and should be rejected. Null and Alternative Hypotheses The null hypothesis (H0) : It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt. The alternative hypothesis (Ha): It is a claim about the population that is contradictory to H0 and what we conclude when we reject H0. 2

3 How to formulate the conclusion The conclusions are made in reference to the null hypothesis. We either reject the null hypothesis, or else we fail to reject the null hypothesis. If we reject the null hypothesis, it means that our data support the alternative hypotheses. If we fail to reject H0, it does not mean that it is proven to be true. It only means that our data fits within its scope. Errors and Correct Decisions Example: buying a laundry detergent. Two choices: Tide and generic detergent VS 3

4 Example: laundry detergents (continued) H0: there is no difference in performance Ha: Tide performs better H0 is true Type A correct decision. Decision: no difference in performance (and it is true). You bought generic product and saved money. Type I error (false positive). Decision: Tide performs better (in reality, no difference) You bought Tide and wasted \$\$ H0 is false Type II error (false negative). Decision: no difference (false, as Tide performs better). You bought generic product, got inferior results. Type B correct decision. Decision: Tide is better (true) You bought Tide and got better results Video on hypothesis testing with example: 4

5 Alpha and beta α is the level of significance of the test It equals the probability of making a type I error. 1 α equals the probability of making type A correct decision β is the probability of making a type II error. 1 β is called the Power of the Test. It equals the probability of making type B correct decision. Hypothesis testing when σ is not known When the population standard deviation, σ, is not known, we use the sample standard deviation, s, instead. And instead of the normal distribution, we use the Student s t distribution. For the classical approach, we will use Table 2 (Critical Values of Student s t Distribution), and for the p-value approach we will use Table 3 (called p-values for Student s t Distribution) with df = n 1 5

6 Hypothesis testing (classical approach) 1. State the hypotheses H0 and Ha. 2. Compute the test statistic t = x μ s n 3. Find the critical value(s) in the table. 4. Draw a bell-shaped curve and indicate the region(s) of rejection. 5. Place the test statistic onto the graph. 6. State your decision. Tails and critical values H a : μ μ 0 a two-tailed test with the critical values ±t( df, α 2) H a : μ > μ 0 a right-tailed test with the critical value t(df, α) H a : μ < μ 0 a left-tailed test with the critical value t(df, α) 6

7 Hypothesis testing (p-value approach) 1. State the hypotheses H0 and Ha. 2. Compute the test statistic t = x μ s n 3. Is this a left-, right-, or a two-tailed test? 4. Find the corresponding p-value in the table. 5. Compare the p-value with the level of significance α. 6. State your decision. What is the p-value? Right-tailed test: the area to the right of t Left-tailed test: the area to the left of t Two-tailed test: twice the area mathcaptain.com 7

8 Comparing the p-value and α: If the p-value is smaller than the level of significance α, it means that the test statistic is in the region of rejection. In this case, decision: reject H0. If the p-value is larger than the level of significance α, it means that the test statistic is in the region of acceptance. In this case, decision: fail to reject H0. Example: right-tailed test A company that makes Orange Soda claims that on the average its soda cans contain no more than 39 grams of sugar. A random sample of 12 cans tested in a lab yielded the following sugar contents (in grams): Can we disprove the company s claim at a 5% level of significance? Assume that the amount of sugar in cans is normally distributed. 8

9 Example: Orange Soda (classical approach) 1. H 0 : μ 39 g H a : μ > 39 g 2. Compute from sample: x = g, s = g Test statistic: t = / 12 = Since α = 0.05, we have the critical value t df, α = t 11, 0.05 = Plot the curve! 5. Where is t? (in the region of rejection) 6. Decision: reject H0 Example: Orange Soda (the p-value approach) 1. H 0 : μ 39 g H a : μ > 39 g 2. Test statistic t = This is a right-tailed test. 4. From Table 3 with df = 11: p-value = (always pick the bigger value) 5. Compare: p-value = < 0.05 = α 6. Decision: Reject H0 9

10 Example: left-tailed test A restaurant owner has counted the number of clients in his restaurant during 14 randomly selected Fridays: He wants to test the claim that the average number of clients in the restaurant on Fridays is actually smaller than 186, using a 2.5% level of significance. Assume that the number of clients is normally distributed. Example: restaurant (classical approach) 1. H 0 : μ 186 H a : μ < Compute from the sample: x = and s = Test statistic: t = = α = 0.025, the critical value: t df, α = t 13, = Plot the curve 5. Where is t? (in the region of acceptance) 6. Decision: Fail to reject H0 10

11 Example: restaurant (the p-value approach) 1. H 0 : μ 186 H a : μ < Test statistic: t = This is a left-tailed test. 4. Use Table 3 to find with df = 13 p-value = (take the larger value) 5. Compare: p-value = > = α 6. Decision: Fail to reject H0 Example: two-tailed test According to a website, the average weekly wage of government workers is \$1038. A sample of randomly chosen 11 government workers is taken and their weekly wages are recorded: \$1080 \$990 \$1540 \$960 \$920 \$880 \$1220 \$1630 \$940 \$1270 \$1160 Test at a 10% level of significance whether the average weekly wage of government workers is actually different from \$1038. Assume a normal distribution of wages. 11

12 Example: wages (classical approach) 1. H 0 : μ = \$1038 H a : μ \$ Compute from the sample: x = \$ and s = \$252.6 Test statistic: t = = α = 0.1, the critical values: ±t df, α/2 = ±t 10, 0.05 = ± Plot the curve 5. Where is t? (in the region of acceptance) 6. Decision: Fail to reject H0 Example: wages (the p-value approach) 1. H 0 : μ = \$1038 H a : μ \$ Test statistic: t = This is a two-tailed test with positive t. 4. Find the p-value from Table 3 with df = 10: p-value = 2 * = (because two-tailed!) 5. Compare: p-value = > 0.1 = α 6. Decision: Fail to reject H0 The decision would be different if we would ve forgotten to multiply by 2. 12

13 Example: practice An article in the San Jose Mercury News claims that students in the California state university system take an average of 4.5 years to finish their undergraduate degrees. Suppose you suspect that the average time is longer. You conduct a survey of 30 students and obtain a sample mean of 4.8 years and a sample standard deviation of 0.9 years. Test the claim at a 5% level of significance. (Do both, the classical, and the p-value approaches.) Example: practice A website claims that in Toronto, the average water/garbage bill for a single family house is \$650 per year. A researcher wants to test this claim by randomly choosing 50 single family houses. The average water/garbage bill in his sample turns out to be equal to \$705 per year with a standard deviation of \$195. Can he claim that the average annual water/garbage bill for a single family house in Toronto is actually different from \$650 at a 2% level of significance? 13

14 Example: practice A telephone company claims that the mean duration of all long-distance phone calls made by its residential customers is at least 11 minutes. Here is a random sample of 16 long-distance calls, in minutes: Assuming the duration of long-distance calls is normally distributed, test at a 10% level of significance whether the mean duration of all long-distance calls is actually less than 11 minutes. 14

Hypothesis Testing. April 21, 2009

Hypothesis Testing April 21, 2009 Your Claim is Just a Hypothesis I ve never made a mistake. Once I thought I did, but I was wrong. Your Claim is Just a Hypothesis Confidence intervals quantify how sure

Wording 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

Lecture Topic 6: Chapter 9 Hypothesis Testing

Lecture Topic 6: Chapter 9 Hypothesis Testing 9.1 Developing Null and Alternative Hypotheses Hypothesis testing can be used to determine whether a statement about the value of a population parameter should

Chapter 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

Hypothesis 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

Hypothesis 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

Section 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

Hypothesis 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

Hypothesis Testing. Bluman Chapter 8

CHAPTER 8 Learning Objectives C H A P T E R E I G H T Hypothesis Testing 1 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 8-5 2 Test for

Chapter 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

The topics in this section concern with the second course objective.

3.2 Hypothesis Testing The topics in this section concern with the second course objective. In practice, a decision is often made according to the result of a statistical analysis, actually a statistical

A 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

I. Basics of Hypothesis Testing

Introduction to Hypothesis Testing This deals with an issue highly similar to what we did in the previous chapter. In that chapter we used sample information to make inferences about the range of possibilities

MULTIPLE 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

Chapter 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

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 p-value of the test

A null hypothesis must always have μ or p, an equal sign, and the claimed value for the parameter in it!

HOSP 1207 (Business Stats) Learning Centre Formal Hypothesis: Making Decisions with a Single Sample This worksheet continues to build on the previous concepts of inferential statistics, only now, we re

6.1 The Elements of a Test of Hypothesis

University of California, Davis Department of Statistics Summer Session II Statistics 13 August 22, 2012 Date of latest update: August 20 Lecture 6: Tests of Hypothesis Suppose you wanted to determine

MCQ TESTING OF HYPOTHESIS

MCQ TESTING OF HYPOTHESIS MCQ 13.1 A statement about a population developed for the purpose of testing is called: (a) Hypothesis (b) Hypothesis testing (c) Level of significance (d) Test-statistic MCQ

Ch. 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

Statistical Inference and t-tests

1 Statistical Inference and t-tests Objectives Evaluate the difference between a sample mean and a target value using a one-sample t-test. Evaluate the difference between a sample mean and a target value

Chapter 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

Math 1 MPS Homework 6 Answers to additional problems 1. What are the two types of hypotheses used in a hypothesis test? How are they related? Ho: Null Hypotheses A statement about a population parameter

MATH 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

Hypothesis 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

Confidence Intervals and Hypothesis Testing

Name: Class: Date: Confidence Intervals and Hypothesis Testing Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The librarian at the Library of Congress

CHAPTER 9 HYPOTHESIS TESTING

CHAPTER 9 HYPOTHESIS TESTING A hypothesis test is a formal way to make a decision based on statistical analysis. A hypothesis test has the following general steps: Set up two contradictory hypotheses.

Probability & 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,

Hypothesis Testing Population Mean

Z-test About One Mean ypothesis Testing Population Mean The Z-test about a mean of population we are using is applied in the following three cases: a. The population distribution is normal and the population

The alternative hypothesis,, is the statement that the parameter value somehow differs from that claimed by the null hypothesis. : 0.5 :>0.5 :<0.

Section 8.2-8.5 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

STA218 Introduction to Hypothesis Testing

STA218 Introduction to Hypothesis Testing Al Nosedal. University of Toronto. Fall 2015 October 29, 2015 Who wants to be a millionaire? Let s say that one of you is invited to this popular show. As you

Hypothesis Testing. Chapter Introduction

Contents 9 Hypothesis Testing 553 9.1 Introduction............................ 553 9.2 Hypothesis Test for a Mean................... 557 9.2.1 Steps in Hypothesis Testing............... 557 9.2.2 Diagrammatic

Chapter 8 Introduction to Hypothesis Testing

Chapter 8 Student Lecture Notes 8-1 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

The 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 " of a normally distributed measurement and to test the goodness

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

Chapter 9: Hypothesis Tests of a Single Population

Chapter 9: Hypothesis Tests of a Single Population Department of Mathematics Izmir University of Economics Week 12 2014-2015 Introduction In this chapter we will focus on Example developing hypothesis

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.

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

A) to D) to B) to E) to C) to Rate of hay fever per 1000 population for people under 25

Unit 0 Review #3 Name: Date:. Suppose a random sample of 380 married couples found that 54 had two or more personality preferences in common. In another random sample of 573 married couples, it was found

Hypothesis Testing: Single Mean and Single Proportion

Chapter 9 Hypothesis Testing: Single Mean and Single Proportion 9.1 Hypothesis Testing: Single Mean and Single Proportion 1 9.1.1 Student Learning Objectives By the end of this chapter, the student should

8-2 Basics of Hypothesis Testing. Definitions. Rare Event Rule for Inferential Statistics. Null Hypothesis

8-2 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

Statistics for Management II-STAT 362-Final Review

Statistics for Management II-STAT 362-Final Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. The ability of an interval estimate to

Null 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

Chapter 9: Hypothesis Testing GBS221, Class April 15, 2013 Notes Compiled by Nicolas C. Rouse, Instructor, Phoenix College

Chapter Objectives 1. Learn how to formulate and test hypotheses about a population mean and a population proportion. 2. Be able to use an Excel worksheet to conduct hypothesis tests about population means

Chapter 9 Introduction to Hypothesis Testing

Chapter 9 Introduction to Hypothesis Testing 9.2 - Hypothesis Testing Hypothesis testing is an eample of inferential statistics We use sample information to draw conclusions about the population from which

Third 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

Chapter 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

Lecture 13: Kolmogorov Smirnov Test & Power of Tests

Lecture 13: Kolmogorov Smirnov Test & Power of Tests S. Massa, Department of Statistics, University of Oxford 2 February 2016 An example Suppose you are given the following 100 observations. -0.16-0.68-0.32-0.85

Hypothesis 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

1 Confidence intervals

Math 143 Inference for Means 1 Statistical inference is inferring information about the distribution of a population from information about a sample. We re generally talking about one of two things: 1.

Hypothesis 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),

Power and Sample Size Determination

Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 Power 1 / 31 Experimental Design To this point in the semester,

Chapter 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

Chapter Five. Hypothesis Testing: Concepts

Chapter Five The Purpose of Hypothesis Testing... 110 An Initial Look at Hypothesis Testing... 112 Formal Hypothesis Testing... 114 Introduction... 114 Null and Alternate Hypotheses... 114 Procedure for

CHAPTER 10: HYPOTHESIS TESTING WITH TWO SAMPLES

CHAPTER 10: HYPOTHESIS TESTING WITH TWO SAMPLES Exercise 1. Exercise 2. Exercise 3. Indicate if the hypothesis test is for a. independent group means, population standard deviations, and/or variances known

Statistics Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Statistics Final Exam Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Assume that X has a normal distribution, and find the indicated

Stat 210 Exam Four. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Stat 210 Exam Four Read these directions carefully. As usual, you may pick any part of one problem to omit by writing OMIT in the answer blank (any one multiple choice or any one part of the other problems).

For instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on the average.

Hypothesis Testing: Single Mean and Single Proportion Introduction One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question

Stats: Test Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Provide an appropriate response. ) Given H0: p 0% and Ha: p < 0%, determine

MAT X Hypothesis Testing - Part I

MAT 2379 3X Hypothesis Testing - Part I Definition : A hypothesis is a conjecture concerning a value of a population parameter (or the shape of the population). The hypothesis will be tested by evaluating

reductio 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

Homework 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

Math 62 Statistics Sample Exam Questions

Math 62 Statistics Sample Exam Questions 1. (10) Explain the difference between the distribution of a population and the sampling distribution of a statistic, such as the mean, of a sample randomly selected

Purpose 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

Hypothesis 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

Unit 21 Student s t Distribution in Hypotheses Testing

Unit 21 Student s t Distribution in Hypotheses Testing Objectives: To understand the difference between the standard normal distribution and the Student's t distributions To understand the difference between

Chapter 8: Hypothesis Testing of a Single Population Parameter

Chapter 8: Hypothesis Testing of a Single Population Parameter THE LANGUAGE OF STATISTICAL DECISION MAKING DEFINITIONS: The population is the entire group of objects or individuals under study, about which

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

Practice Set 8b ST Spring 2014

Practice Set 8b ST 20 - Spring 204 The following problem set will help you work with hypothesis testing.. Ex 8.7 (p. 400. Add the following parts: (c Explain why the assumption that interpupillary distance

Null and Alternative Hypotheses

OpenStax-CNX module m47033 1 Null and Alternative Hypotheses OpenStax College This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 3.0 The actual test begins

Connexions module: m

Connexions module: m17025 1 Hypothesis Testing: Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Unknown Population Standard Deviations Susan Dean Barbara

Hypothesis 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

Power & Effect Size power Effect Size

Power & Effect Size Until recently, researchers were primarily concerned with controlling Type I errors (i.e. finding a difference when one does not truly exist). Although it is important to make sure

One-Sample t-test. Example 1: Mortgage Process Time. Problem. Data set. Data collection. Tools

One-Sample t-test Example 1: Mortgage Process Time Problem A faster loan processing time produces higher productivity and greater customer satisfaction. A financial services institution wants to establish

AMS 5 HYPOTHESIS TESTING

AMS 5 HYPOTHESIS TESTING Hypothesis Testing Was it due to chance, or something else? Decide between two hypotheses that are mutually exclusive on the basis of evidence from observations. Test of Significance

Chapter 8: Introduction to Hypothesis Testing

Chapter 8: Introduction to Hypothesis Testing We re now at the point where we can discuss the logic of hypothesis testing. This procedure will underlie the statistical analyses that we ll use for the remainder

Statistiek I. t-tests. John Nerbonne. CLCG, Rijksuniversiteit Groningen. John Nerbonne 1/35

Statistiek I t-tests John Nerbonne CLCG, Rijksuniversiteit Groningen http://wwwletrugnl/nerbonne/teach/statistiek-i/ John Nerbonne 1/35 t-tests To test an average or pair of averages when σ is known, we

Testing: 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

Introductory Statistics Hypothesis Testing Review( Critical Value Approach)

MULTIPLE CHOICE. Introductory Statistics Hypothesis Testing Review( Critical Value Approach) Determine the critical value(s) for a one-mean z-test. 1) A left-tailed test with α = 0.02. A) ±1.96 B) ±2.054

Classical Hypothesis Testing and GWAS

Department of Computer Science Brown University, Providence sorin@cs.brown.edu September 15, 2014 Outline General Principles Classical statistical hypothesis testing involves the test of a null hypothesis

Math 251: Practice Questions for Test III Hints and Answers.. Then. P (67 x 69) = P (.33 z.33) = =.2586.

Math 251: Practice Questions for Test III Hints and Answers III.A: The Central Limit Theorem and Sampling Distributions. III.A.1 The heights of 18-year-old men are approximately normally distributed with

Hypothesis Testing Level I Quantitative Methods. IFT Notes for the CFA exam

Hypothesis Testing 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 3 2. Hypothesis Testing... 3 3. Hypothesis Tests Concerning the Mean... 10 4. Hypothesis Tests

Tests of Hypotheses: Means

Tests of Hypotheses: Means We often use inferential statistics to make decisions or judgments about the value of a parameter, such as a population mean. For example, we might need to decide whether the

Unit 24 Hypothesis Tests about Means

Unit 24 Hypothesis Tests about Means Objectives: To recognize the difference between a paired t test and a two-sample t test To perform a paired t test To perform a two-sample t test A measure of the amount

1. What are the two types of hypotheses used in a hypothesis test? How are they related?

Math 10 - Homework 6 Part A 1. What are the two types of hypotheses used in a hypothesis test? How are they related? 2. Describe the two types of error possible in a hypothesis test decision. True or False?

Introduction 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

Hypothesis Testing 1

Hypothesis Testing 1 Statistical procedures for addressing research questions involves formulating a concise statement of the hypothesis to be tested. The hypothesis to be tested is referred to as the

Chapter 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 gender-selection method developed by Genetics

5/31/2013. 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.

Hypothesis Testing. Chapter 7

Hypothesis Testing Chapter 7 Hypothesis Testing Time to make the educated guess after answering: What the population is, how to extract the sample, what characteristics to measure in the sample, After

E205 Final: Version B

Name: Class: Date: E205 Final: Version B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of a local nightclub has recently surveyed a random

An Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 9 - FUNDAMENTALS OF HYPOTHESIS TESTING: ONE-SAMPLE TESTS

The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 302) Spring Semester 20 Chapter 9 - FUNDAMENTALS OF HYPOTHESIS

6/19/13 Practice problems on ch 8 and ch 11

6/19/13 Practice problems on ch 8 and ch 11 For all hypotheses test you must do the following: z/t test a. State the hypotheses and identify the claim. b. Find the critical values. c. Compute the test

The calculations lead to the following values: d 2 = 46, n = 8, s d 2 = 4, s d = 2, SEof d = s d n s d n

EXAMPLE 1: Paired t-test and t-interval DBP Readings by Two Devices The diastolic blood pressures (DBP) of 8 patients were determined using two techniques: the standard method used by medical personnel

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

STATISTICS/GRACEY EXAM 3 PRACTICE/CH. 8-9 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the P-value for the indicated hypothesis test. 1) A

Math 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,

9.1 Hypothesis Testing

9.1 Hypothesis Testing Define: 1. Null Hypothesis 2. Alternative Hypothesis Null Hypothesis: H 0, statement that the population proportion, or population mean is EQUAL TO a number population proportion

Hypothesis Testing. Dr. Bob Gee Dean Scott Bonney Professor William G. Journigan American Meridian University

Hypothesis Testing Dr. Bob Gee Dean Scott Bonney Professor William G. Journigan American Meridian University 1 AMU / Bon-Tech, LLC, Journi-Tech Corporation Copyright 2015 Learning Objectives Upon successful

Measuring the Power of a Test

Textbook Reference: Chapter 9.5 Measuring the Power of a Test An economic problem motivates the statement of a null and alternative hypothesis. For a numeric data set, a decision rule can lead to the rejection