Name: (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%.

Size: px
Start display at page:

Download "Name: (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%."

Transcription

1 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 or distribution used where applicable!! List the applicable formula, even if a calculator program was used, and list all quantities/variables. 1. Finding the Minimum Sample Size (2 points each) (a) Find the minimum sample size required to estimate an unknown population mean µ, with a margin of error of $57, confidence level 98%, and σ = $326. (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%. 2. Critical Values (3 points each) (a) Find the critical value when estimating population mean µ, for a sample size n = 37 and a confidence level of 96%, when σ is known. (b) Find the critical value when estimating a population proportion for a sample size n = 50 and a confidence level of 99%.

2 3. Margin of Error, E and point estimate (2 points each) (a) The following confidence interval is obtained for a population proportion: < p < Find the margin of error, E and a point estimate for p, ˆp. E = ˆp = (b) Find the margin of error, E for a 90% confidence interval for µ, when n = 100, x = 525, and s = 45. E = Page 2

3 4. Confidence Intervals (6 points each) I Assume all requirements needed to construct the confidence interval are met. II List the applicable formula, even if a calculator program was used. III List the calculator program used, and all quantities/variables. IV Construct the confidence interval. V Be sure to interpret each Confidence Interval and answer all questions! (a) Medical Malpractice An important issue facing Americans is the large number of medical malpractice lawsuits and the expenses that they generate. In a study of 1228 randomly selected medical malpractice lawsuits, it is found that 856 of them were later dropped or dismissed (based on data from the Physician Insurers Association of America). (i) Construct a 99% confidence interval estimate of the proportion of medical malpractice lawsuits that are dropped or dismissed. (ii) Does it appear that the majority of such suits are dropped or dismissed? (b) Thirty randomly selected students took the statistics final exam. The standard deviation for such exams is known to be 6.5 points. If the sample mean was 78.5 points and the sample standard deviation was 7 points, construct a 96% confidence interval for the mean score of all statistics students. Page 3

4 (c) Eat your spinach Six measurements were made of the mineral content (in percent) of spinach, with the results listed below. It is reasonable to assume that the population is approximately normal. (i) Construct a 95% confidence interval for the mean mineral content. (ii) Based on the confidence interval, is it reasonable to believe that the mean mineral content of spinach may be greater than 21%? Explain. (Source: Journal of Nutrition 66:5566) State and explain whether the hypothesis test involves a sampling distribution that is a Normal distribution, Student s t distribution, Chi-square distribution or neither. Assume all samples are simple random samples. Work without explanation is incorrect. (6 points) (a) Claim: µ = 7.6. Sample data: n = 28, x = 13.1, s = 3.2. The sample data appear to come from a normally distributed population. (b) Claim: µ > 122. Sample data: n = 17, x = 135, s = The sample data appear to come from a population with a very skewed distribution. (c) Claim: σ Sample data: n = 33, s = The sample data comes from a normally distributed population. Page 4

5 6. State the hypotheses Express the claim into a null or alternative hypothesis, and state the other hypothesis as well. Indicate which of the two hypotheses represents the claim. (3 points each) (a) Kids with cell phones: A marketing manager for a cell phone company claims that more than 35% of children aged 1011 have cell phones. H 0 : H 1 : claim is represented by H 0 / H 1 (circle one) (b) Big fish: Scientists want to perform a hypothesis test to determine how strong the evidence is that the mean weight of a certain species of flounder differs from 20 grams. H 0 : H 1 : claim is represented by H 0 / H 1 (circle one) 7. Critical Values (4 points each) (a) Assume that the data has a normal distribution and the number of observations is 36. Find the critical value(s), z used to test a null hypothesis µ = 0.73, α = 0.04 for a two-tailed test. (b) Find the critical value(s), χ 2 L and/or χ 2 R used to test H 1 : σ < 7.5, n = 18, and α = Test Statistic Use the given information to find the value of the test statistic. Make sure you name it correctly. (4 points each) (a) Carbon Monoxide Detectors The claim is that less than 1 of adults in the 2 United States have carbon monoxide detectors. A KRC Research survey of 1005 adults resulted in 462 who have carbon monoxide detectors. Page 5

6 (b) Find the value of the test statistic, where H 1 : µ > 17, x = 20.5, n = 7, and s = P -value Use the given information to find the P-value. (4 points each) (a) The test statistic in a left-tailed test is z = 1.67 (b) The test statistic in a two-tailed test is t = Type I and Type II Errors A publisher of a local newspaper claims that the percentage of year-olds who read a daily newspaper is greater than 15%. Assume that a hypothesis test of the given claim will be conducted. Identify the Type I and Type II errors for the given claim. (3 points each) (a) State the Type I Error for the test above: (b) State the Type II Error for the test above: Page 6

7 11. Hypothesis Testing Assume that a simple random sample has been selected from a normally distributed population. Find and state the: I Null and alternative hypothesis II List all given variables used III Perform the calculations and list the calculator program used, and all quantities/variables from that program. IV Draw a picture of the distribution, showing your test statistic or P -value, and make your comparison. V State the final conclusion using the original claim. (8 points each) (a) Heavy children: Are children heavier now than they were in the past? The National Health and Nutrition Examination Survey (NHANES) taken between 1999 and 2002 reported that the mean weight of six-year-old girls in the United States was 49.3 pounds. Another NHANES survey, published in 2008, reported that a sample of 193 six-year-old girls weighed between 2003 and 2006 had an average weight of 51.5 pounds. Assume the population standard deviation is σ = 15 pounds. Can you conclude that the mean weight of six-year-old girls is higher in 2006 than in 2002? Use the α = 0.01 level of significance. Page 7

8 (b) Google it: The marketing research company comscore, Inc. reported that 65% of online searches in March 2010 used Google as the search engine. A network administrator wants to determine whether the percentage of searches that use Google is different in his company. He samples 400 searches and nds that 295 of them use Google. Can he conclude that the percentage of searches that use Google in his company differs from 65%? Use the α = 0.04 level of significance. Page 8

9 (c) Playing Times of Popular Songs Listed below are the playing times (in seconds) of songs that were popular at the time of this writing. (The songs are by Timberlake, Furtado, Daughtry, Stefani, Fergie, Akon, Ludacris, Beyonce, Nickelback, Rihanna, Fray, Lavigne, Pink, Mims, Mumidee, and Omarion.) Use a α = 0.05 significance level to test the claim that the songs are from a population with a standard deviation less than one minute A battery manufacturer claims that a recently developed calculator battery has a mean life longer than 100 hours. Assuming that a hypothesis test has been conducted, and that the conclusion is to reject the null hypothesis, state the final conclusion using the original claim. (2 points) 13. EXTRA CREDIT You can increase the width of a confidence interval by... (circle one) (4 points) A. increasing the confidence level or increasing the sample size B. increasing the confidence level or decreasing the sample size C. decreasing the confidence level or increasing the sample size D. decreasing the confidence level or decreasing the sample size Page 9

November 08, 2010. 155S8.6_3 Testing a Claim About a Standard Deviation or Variance

November 08, 2010. 155S8.6_3 Testing a Claim About a Standard Deviation or Variance Chapter 8 Hypothesis Testing 8 1 Review and Preview 8 2 Basics of Hypothesis Testing 8 3 Testing a Claim about a Proportion 8 4 Testing a Claim About a Mean: σ Known 8 5 Testing a Claim About a Mean: σ

More information

Chapter Additional: Standard Deviation and Chi- Square

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

More information

Hypothesis testing: Examples. AMS7, Spring 2012

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

More information

Chapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing

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 information

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) 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 information

Basic Statistics Self Assessment Test

Basic Statistics Self Assessment Test Basic Statistics Self Assessment Test Professor Douglas H. Jones PAGE 1 A soda-dispensing machine fills 12-ounce cans of soda using a normal distribution with a mean of 12.1 ounces and a standard deviation

More information

Introduction to Hypothesis Testing. Hypothesis Testing. Step 1: State the Hypotheses

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

More information

HypoTesting. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

HypoTesting. 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 information

HYPOTHESIS TESTING: POWER OF THE TEST

HYPOTHESIS 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 information

9.1 Basic Principles of Hypothesis Testing

9.1 Basic Principles of Hypothesis Testing 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

More information

12.5: CHI-SQUARE GOODNESS OF FIT TESTS

12.5: 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 information

CHAPTER 11 SECTION 2: INTRODUCTION TO HYPOTHESIS TESTING

CHAPTER 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 information

Lecture 13 More on hypothesis testing

Lecture 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 information

Wording of Final Conclusion. Slide 1

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

More information

Confidence Intervals (Review)

Confidence Intervals (Review) Intro to Hypothesis Tests Solutions STAT-UB.0103 Statistics for Business Control and Regression Models Confidence Intervals (Review) 1. Each year, construction contractors and equipment distributors from

More information

9-3.4 Likelihood ratio test. Neyman-Pearson lemma

9-3.4 Likelihood ratio test. Neyman-Pearson lemma 9-3.4 Likelihood ratio test Neyman-Pearson lemma 9-1 Hypothesis Testing 9-1.1 Statistical Hypotheses Statistical hypothesis testing and confidence interval estimation of parameters are the fundamental

More information

Chapter 8. Hypothesis Testing

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 information

STAT 3090 Test 3 - Version A Fall 2015

STAT 3090 Test 3 - Version A Fall 2015 Multiple Choice: (Questions 1-16) Answer the following questions on the scantron provided using a #2 pencil. Bubble the response that best answers the question. Each multiple choice correct response is

More information

Stats Review Chapters 9-10

Stats 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 information

Hypothesis Testing. Bluman Chapter 8

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

More information

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

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 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 information

How to Conduct a Hypothesis Test

How 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 information

3.4 Statistical inference for 2 populations based on two samples

3.4 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 information

Hypothesis Testing --- One Mean

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

More information

Chapter Five: Paired Samples Methods 1/38

Chapter 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 information

1) What is the probability that the random variable has a value greater than 2? A) 0.750 B) 0.625 C) 0.875 D) 0.700

1) What is the probability that the random variable has a value greater than 2? A) 0.750 B) 0.625 C) 0.875 D) 0.700 Practice for Chapter 6 & 7 Math 227 This is merely an aid to help you study. The actual exam is not multiple choice nor is it limited to these types of questions. Using the following uniform density curve,

More information

Chapter III. Testing Hypotheses

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

More information

Practice problems for Homework 12 - confidence intervals and hypothesis testing. Open the Homework Assignment 12 and solve the problems.

Practice problems for Homework 12 - confidence intervals and hypothesis testing. Open the Homework Assignment 12 and solve the problems. Practice problems for Homework 1 - confidence intervals and hypothesis testing. Read sections 10..3 and 10.3 of the text. Solve the practice problems below. Open the Homework Assignment 1 and solve the

More information

Solutions to Worksheet on Hypothesis Tests

Solutions to Worksheet on Hypothesis Tests s to Worksheet on Hypothesis Tests. A production line produces rulers that are supposed to be inches long. A sample of 49 of the rulers had a mean of. and a standard deviation of.5 inches. The quality

More information

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 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 information

A Trial Analogy for Statistical. Hypothesis Testing. Legal Trial Begin with claim: Statistical Significance Test Hypotheses (statements)

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

More information

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Open book and note Calculator OK Multiple Choice 1 point each MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data.

More information

BA 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 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 information

Chapter 8 Introduction to Hypothesis Testing

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

More information

A) 0.1554 B) 0.0557 C) 0.0750 D) 0.0777

A) 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 information

The Goodness-of-Fit Test

The Goodness-of-Fit Test on the Lecture 49 Section 14.3 Hampden-Sydney 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 information

Chapter 9, Part A Hypothesis Tests. Learning objectives

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

More information

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

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

More information

Math 251, Review Questions for Test 3 Rough Answers

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,

More information

An Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10- TWO-SAMPLE TESTS

An 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 information

Lecture Topic 6: Chapter 9 Hypothesis Testing

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

More information

STA 2023H Solutions for Practice Test 4

STA 2023H Solutions for Practice Test 4 1. Which statement is not true about confidence intervals? A. A confidence interval is an interval of values computed from sample data that is likely to include the true population value. B. An approximate

More information

Construct a scatterplot for the given data. 2) x Answer:

Construct a scatterplot for the given data. 2) x Answer: Review for Test 5 STA 2023 spr 2014 Name Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents

More information

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

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

More information

Chapter 7 Notes - Inference for Single Samples. You know already for a large sample, you can invoke the CLT so:

Chapter 7 Notes - Inference for Single Samples. You know already for a large sample, you can invoke the CLT so: Chapter 7 Notes - Inference for Single Samples You know already for a large sample, you can invoke the CLT so: X N(µ, ). Also for a large sample, you can replace an unknown σ by s. You know how to do a

More information

Hypothesis Testing COMP 245 STATISTICS. Dr N A Heard. 1 Hypothesis Testing 2 1.1 Introduction... 2 1.2 Error Rates and Power of a Test...

Hypothesis Testing COMP 245 STATISTICS. Dr N A Heard. 1 Hypothesis Testing 2 1.1 Introduction... 2 1.2 Error Rates and Power of a Test... Hypothesis Testing COMP 45 STATISTICS Dr N A Heard Contents 1 Hypothesis Testing 1.1 Introduction........................................ 1. Error Rates and Power of a Test.............................

More information

In the general population of 0 to 4-year-olds, the annual incidence of asthma is 1.4%

In the general population of 0 to 4-year-olds, the annual incidence of asthma is 1.4% Hypothesis Testing for a Proportion Example: We are interested in the probability of developing asthma over a given one-year period for children 0 to 4 years of age whose mothers smoke in the home In the

More information

General 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. 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 information

CHAPTER 9 HYPOTHESIS TESTING

CHAPTER 9 HYPOTHESIS TESTING CHAPTER 9 HYPOTHESIS TESTING The TI-83 Plus and TI-84 Plus fully support hypothesis testing. Use the key, then highlight TESTS. The options used in Chapter 9 are given on the two screens. TESTING A SINGLE

More information

Null Hypothesis H 0. The null hypothesis (denoted by H 0

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

More information

Two Related Samples t Test

Two Related Samples t Test Two Related Samples t Test In this example 1 students saw five pictures of attractive people and five pictures of unattractive people. For each picture, the students rated the friendliness of the person

More information

Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation

Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation Parkland College A with Honors Projects Honors Program 2014 Calculating P-Values Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating P-Values" (2014). A with Honors Projects.

More information

7 Hypothesis testing - one sample tests

7 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 information

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

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

More information

PROBLEM 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. 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

More information

5/31/2013. Chapter 8 Hypothesis Testing. Hypothesis Testing. Hypothesis Testing. Outline. Objectives. Objectives

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.

More information

C. The null hypothesis is not rejected when the alternative hypothesis is true. A. population parameters.

C. 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 information

Introduction 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. 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 information

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS 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 information

4) The role of the sample mean in a confidence interval estimate for the population mean is to: 4)

4) 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 information

Hypothesis Testing: Two Means, Paired Data, Two Proportions

Hypothesis 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 information

Name: Date: D) 3141 3168

Name: Date: D) 3141 3168 Name: Date: 1. A sample of 25 different payroll departments found that the employees worked an average of 310.3 days a year with a standard deviation of 23.8 days. What is the 90% confidence interval for

More information

Final Exam Practice Problem Answers

Final Exam Practice Problem Answers Final Exam Practice Problem Answers The following data set consists of data gathered from 77 popular breakfast cereals. The variables in the data set are as follows: Brand: The brand name of the cereal

More information

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS 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 information

Practice Exam. 1. What is the median of this data? A) 64 B) 63.5 C) 67.5 D) 59 E) 35

Practice Exam. 1. What is the median of this data? A) 64 B) 63.5 C) 67.5 D) 59 E) 35 Practice Exam Use the following to answer questions 1-2: A census is done in a given region. Following are the populations of the towns in that particular region (in thousands): 35, 46, 52, 63, 64, 71,

More information

13.2 The Chi Square Test for Homogeneity of Populations The setting: Used to compare distribution of proportions in two or more populations.

13.2 The Chi Square Test for Homogeneity of Populations The setting: Used to compare distribution of proportions in two or more populations. 13.2 The Chi Square Test for Homogeneity of Populations The setting: Used to compare distribution of proportions in two or more populations. Data is organized in a two way table Explanatory variable (Treatments)

More information

CHAPTER 11 CHI-SQUARE AND F DISTRIBUTIONS

CHAPTER 11 CHI-SQUARE AND F DISTRIBUTIONS CHAPTER 11 CHI-SQUARE AND F DISTRIBUTIONS CHI-SQUARE TESTS OF INDEPENDENCE (SECTION 11.1 OF UNDERSTANDABLE STATISTICS) In chi-square tests of independence we use the hypotheses. H0: The variables are independent

More information

Chapter 7 - Practice Problems 1

Chapter 7 - Practice Problems 1 Chapter 7 - Practice Problems 1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Define a point estimate. What is the

More information

Chris Slaughter, DrPH. GI Research Conference June 19, 2008

Chris Slaughter, DrPH. GI Research Conference June 19, 2008 Chris Slaughter, DrPH Assistant Professor, Department of Biostatistics Vanderbilt University School of Medicine GI Research Conference June 19, 2008 Outline 1 2 3 Factors that Impact Power 4 5 6 Conclusions

More information

1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1. 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 information

Chapter 1 Hypothesis Testing

Chapter 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 information

Hypothesis Testing or How to Decide to Decide Edpsy 580

Hypothesis Testing or How to Decide to Decide Edpsy 580 Hypothesis Testing or How to Decide to Decide Edpsy 580 Carolyn J. Anderson Department of Educational Psychology University of Illinois at Urbana-Champaign Hypothesis Testing or How to Decide to Decide

More information

MATH 214 (NOTES) Math 214 Al Nosedal. Department of Mathematics Indiana University of Pennsylvania. MATH 214 (NOTES) p. 1/6

MATH 214 (NOTES) Math 214 Al Nosedal. Department of Mathematics Indiana University of Pennsylvania. MATH 214 (NOTES) p. 1/6 MATH 214 (NOTES) Math 214 Al Nosedal Department of Mathematics Indiana University of Pennsylvania MATH 214 (NOTES) p. 1/6 "Pepsi" problem A market research consultant hired by the Pepsi-Cola Co. is interested

More information

Section 12.2, Lesson 3. What Can Go Wrong in Hypothesis Testing: The Two Types of Errors and Their Probabilities

Section 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 information

Name: Date: Use the following to answer questions 3-4:

Name: 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 information

Test of proportion = 0.5 N Sample prop 95% CI z- value p- value (0.400, 0.466)

Test of proportion = 0.5 N Sample prop 95% CI z- value p- value (0.400, 0.466) STATISTICS FOR THE SOCIAL AND BEHAVIORAL SCIENCES Recitation #10 Answer Key PROBABILITY, HYPOTHESIS TESTING, CONFIDENCE INTERVALS Hypothesis tests 2 When a recent GSS asked, would you be willing to pay

More information

Confidence Interval: pˆ = E = Indicated decision: < p <

Confidence 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 information

LAB 4 ASSIGNMENT CONFIDENCE INTERVALS AND HYPOTHESIS TESTING. Using Data to Make Decisions

LAB 4 ASSIGNMENT CONFIDENCE INTERVALS AND HYPOTHESIS TESTING. Using Data to Make Decisions LAB 4 ASSIGNMENT CONFIDENCE INTERVALS AND HYPOTHESIS TESTING This lab assignment will give you the opportunity to explore the concept of a confidence interval and hypothesis testing in the context of a

More information

Non-Parametric Tests (I)

Non-Parametric Tests (I) Lecture 5: Non-Parametric Tests (I) KimHuat LIM lim@stats.ox.ac.uk http://www.stats.ox.ac.uk/~lim/teaching.html Slide 1 5.1 Outline (i) Overview of Distribution-Free Tests (ii) Median Test for Two Independent

More information

Chi-Square Test. Contingency Tables. Contingency Tables. Chi-Square Test for Independence. Chi-Square Tests for Goodnessof-Fit

Chi-Square Test. Contingency Tables. Contingency Tables. Chi-Square Test for Independence. Chi-Square Tests for Goodnessof-Fit Chi-Square Tests 15 Chapter Chi-Square Test for Independence Chi-Square Tests for Goodness Uniform Goodness- Poisson Goodness- Goodness Test ECDF Tests (Optional) McGraw-Hill/Irwin Copyright 2009 by The

More information

AP STATISTICS 2012 SCORING GUIDELINES

AP STATISTICS 2012 SCORING GUIDELINES 2012 SCORING GUIDELINES Question 4 Intent of Question The primary goal of this question was to assess students ability to identify, set up, perform, and interpret the results of an appropriate hypothesis

More information

BUS/ST 350 Exam 3 Spring 2012

BUS/ST 350 Exam 3 Spring 2012 BUS/ST 350 Exam 3 Spring 2012 Name Lab Section ID # INSTRUCTIONS: Write your name, lab section #, and ID# above. Note the statement at the bottom of this page that you must sign when you are finished with

More information

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

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

More information

Math 140 (4,5,6) Sample Exam II Fall 2011

Math 140 (4,5,6) Sample Exam II Fall 2011 Math 140 (4,5,6) Sample Exam II Fall 2011 Provide an appropriate response. 1) In a sample of 10 randomly selected employees, it was found that their mean height was 63.4 inches. From previous studies,

More information

Sampling and Hypothesis Testing

Sampling 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 information

AP Statistics 2002 Scoring Guidelines

AP Statistics 2002 Scoring Guidelines AP Statistics 2002 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought

More information

Less Stress More Success Maths Leaving Cert Higher Level Paper 2

Less Stress More Success Maths Leaving Cert Higher Level Paper 2 Less Stress More Success Maths Leaving Cert Higher Level Paper 2 Revised pages for Chapter 13 Statistics IV: The Normal Curve, z -Scores, Hypothesis Testing and Simulation 228 LESS STRESS MORE SUCCESS

More information

Hypothesis testing for µ:

Hypothesis 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 information

Statistics 2014 Scoring Guidelines

Statistics 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 information

LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

LAB 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 information

Chapter 2. Hypothesis testing in one population

Chapter 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 information

Hypothesis. Testing Examples and Case Studies. Chapter 23. Copyright 2005 Brooks/Cole, a division of Thomson Learning, Inc.

Hypothesis. Testing Examples and Case Studies. Chapter 23. Copyright 2005 Brooks/Cole, a division of Thomson Learning, Inc. Hypothesis Chapter 23 Testing Examples and Case Studies Copyright 2005 Brooks/Cole, a division of Thomson Learning, Inc. 23.1 How Hypothesis Tests Are Reported in the News 1. Determine the null hypothesis

More information

Probability, Binomial Distributions and Hypothesis Testing Vartanian, SW 540

Probability, 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 information

AP STATISTICS (Warm-Up Exercises)

AP 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 information

Third Midterm Exam (MATH1070 Spring 2012)

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

More information

E205 Final: Version B

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

More information

Chapter 16 Multiple Choice Questions (The answers are provided after the last question.)

Chapter 16 Multiple Choice Questions (The answers are provided after the last question.) Chapter 16 Multiple Choice Questions (The answers are provided after the last question.) 1. Which of the following symbols represents a population parameter? a. SD b. σ c. r d. 0 2. If you drew all possible

More information

15.0 More Hypothesis Testing

15.0 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 information

Correlational Research

Correlational 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 information

Statistics 641 - EXAM II - 1999 through 2003

Statistics 641 - EXAM II - 1999 through 2003 Statistics 641 - EXAM II - 1999 through 2003 December 1, 1999 I. (40 points ) Place the letter of the best answer in the blank to the left of each question. (1) In testing H 0 : µ 5 vs H 1 : µ > 5, the

More information