Stats Review Chapters 9-10

Size: px
Start display at page:

Download "Stats Review Chapters 9-10"

Transcription

1 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 Generator from Pearson Revised 1/13

2 Note: This review is composed of questions the textbook and the test generator. This review is meant to highlight basic concepts from the course. It does not cover all concepts presented by your instructor. Refer back to your notes, unit objectives, handouts, etc. to further prepare for your exam. A copy of this review can be found at The final answers are displayed in red and the chapter/section number is the corner.

3 9.1 Confidence Interval for Population Proportion In a survey of 10 musicians, were found to be lefthanded. Is it practical to construct the 90% confidence interval for the population proportion, p? Condition 1: n(.05) N The sample size is less than 5% of the population, so the condition is met. Condition : np(1-p) 10 p= /10=., so np(1-p)=10(.)(1-.)=1.6. This is less than 10 so this condition is not met. So it would not be practical to construct the confidence interval.

4 Confidence Interval for Population Proportion A poll conducted found that 944 of 1748 adults do not believe that people with tattoos are more rebellious. If appropriate construct a 90% confidence interval. Is it appropriate? Yes, it satisfies both conditions. 9.1

5 9.1 Confidence Interval for Population Proportion What is the point estimate? p = 944 = Find z α/. First take 1.90 =.05 The corresponding z-value is We will ignore the negative and just use Find the Margin of Error p(1 p) E = z α/ = (1.54) =.0196 n 1748 Take the point estimate and add/subtract the margin of error =.504, =.5596 The confidence interval is (.504,.5596)

6 9.1 Common z α/ values Confidence Level Z-value 90% % %.576

7 9.1 Sample Size Needed of Population Proportion A researcher wants to estimate the proportion of Americans that have sleep deprivation. How large a sample is needed in order to be 95% confident within 5% if a) the researcher used a previous estimate of 60%? b) the researcher doesn t use a previous estimate?

8 9.1 Sample Size Needed of Population Proportion a) What is the sample size if the researcher used a previous estimate of 60%? N = p 1 p zα E = = 369 b) What is the sample size if the researcher doesn t use a previous estimate? N =.5 zα E = = 385

9 9.1, Find the t-value Find the t-value (using the table) Right tail=.1, n=6 Degrees of Freedom (df)=n-1=5, t= Left tail=.05 n=16 df=15, t= (t is negative for left tail) 90% confidence, n=1 df=0, 1.90 =.05, t = % Confidence, n=83 df= 8 (this is not in the table so choose the closest one: 80), 1.95 =.05, t = % Confidence, n=100 df=1199, since this is more than 1000, we use the z-value 1.99 =.005, t or z =.576

10 9. Estimating a population mean In a sample of 81 SARS patients, the mean incubation period was 4.6 days with a standard deviation of 15.9 days. Construct a 95% confident interval. We cannot use z because we do not have the population standard deviation. Find t α/ : 1.95 =.05, degrees of freedom =n-1= The corresponding t-value is 1.99 Find the Margin of Error s 15.9 E = t α/ = 1.99 n 81 = Add/subtract the margin of error from the sample mean =1.084, =8.116 We are 95% confident that the mean incubation period for SARS patients is between and

11 9. Sample Size for Estimating Population Mean How large must a sample be in order to be 95% confident within points given a sample standard deviation of 13.67? n = zα E s = = 175

12 9.1- What Happens to the Width of the Confidence Interval As the sample size increases The width decreases As the level of confidence increase The width Increases To find out which margin of error is smaller (smaller width) with different sample sizes and level of confidence when everything else is the same calculate z α/ (for proportion) or t α/ (for mean) for both n n cases to see which is smaller.

13 9. Reasonable Interpretation of Confidence Intervals A 90% confidence interval for the hours that college students sleep during the weekday is (7.8, 8.8). Which interpretations are correct? a) 90% of college students sleep between 7.8 and 8.8 hours Flawed: makes an implication about individuals rather than the mean b) We re 90% confident that the mean number of hours of sleep that college students get any day of the week is between 7.8 and 8.8 hours Flawed: should be about the weekday, not any day of the week

14 9. Reasonable Interpretation of Confidence Intervals A 90% confidence interval for the hours that college students sleep during the weekday is (7.8, 8.8). Which interpretations are correct? c) There is a 90% probability that the mean hours of sleep that college students get during a weekday is between 7.8 and 8.8 hours. Flawed: implies the population mean varies rather than the interval d) We re 90% confident that the mean number of hours of sleep that college students during a weekday is between 7.8 and 8.8 hours. Correct!

15 9.3 Find χ 1 α/ Find the Chi-Squared Values andχ α/ 90% confidence, n=0 α=1-.90=.1; df=n-1=19 χ 1 α/ χ α/ = χ 1.1/ = χ.1/ = χ.95 = = χ.05 = % confidence, n=5 α=1-.95=.05; df=n-1=4 χ 1 α/ χ α/ = χ 1.05/ = χ..05/ = χ.975 = = χ.05 = If the degrees of freedom is not on the table, use the closest degrees of freedom If the degrees of freedom is directly between values, find the mean of the values. Ex: For 65, take the χ values for both 60 and 70 and averge their χ values.

16 9.3 Estimating a Population Standard Deviation A student randomly selects 10 paperbacks at a store. The mean price is $8.75 with a standard deviation of $1.50. Construct a 95% confidence interval for the population standard deviation, σ. Assume the data are normally distributed 1. Find χ 1 α/ andχ α/ for 95% confidence level and df=9 χ 1.05/ χ.05/ =.7 = Find the lower and upper bounds of σ Lower: (n 1)s χ = (10 1)1.5 α/ Upper: (n 1)s χ 1 α/ = (10 1)1.5.7 =7.5 = Since we want the confidence interval for σ and we have the lower/upper bounds of σ, we need to take the square roots of the lower and upper bound. Lower: 1.065=1.03 Upper: 7.5=.74 The confidence interval is (1.03,.74)

17 Which Procedure to Use? Copyright 013 Pearson Higher Ed 9.4

18 Hypothesis Testing Determine if it is a right-, left-, or two-tailed test H o : μ = 6 H 1 : μ > 6 H o : μ = 6 H 1 : μ 6 H o : μ = 6 H 1 : μ < 6 Right -tailed Two -tailed Left -tailed The mean age of lawyers in New York is 50.7 years. Two-tailed The mean annual return for an employee's IRA is at most 3.4 percent. Left-Tailed A popular referendum on the ballot is favored by more than half of the voters. Right-Tailed 10.1

19 Type I and Type II errors Determine the type I and type II error. Find the probability of making a type I error. A referendum for an upcoming election is favored by more than half of the voters. Level of Significance, α, is Type I error: rejecting that p=.5, when in reality p 5. Type II error: not rejecting p=.5, when p>.5. Probability(type I error)=α=

20 10.1 Proper Conclusion for Hypothesis Test A candidate for state representative of a certain state claims to be favored by at least half of the voters. If a hypothesis test is preformed, how should you interpret a decision that fails to reject the null hypothesis? A) There is not sufficient evidence to reject the claim p.5. Correct! B) There is sufficient evidence to support the claim p.5. C) There is sufficient evidence to reject the claim p.5. D) There is not sufficient evidence to support the claim p.5.

21 Hypothesis Test for Population Proportion: Classical Approach A survey of 1000 adults, 54 found that they could not eat just one m&m. Does this sample evidence find that more than half of adults can not eat just one m&m. Use the α=.05 level of significance. 1. State the null and alternative Hypothesis H 0 : μ =.5 H 1 : μ >.5. Find p : p = x n = =

22 Hypothesis Test for Population Proportion: Classical Approach 3. Compute the test statistic, z 0 z 0 = p p = p(1 p) n.54.5 =.66.5(1.5) Determine the critical value For right tailed, z α =z.05 = Compare with the test statistic with the critical value For a right-tailed, we reject the null hypothesis if z 0 > z α.66>1.64 Therefore we reject the null hypothesis. 6. Conclusion: We reject the null hypothesis. There is sufficient evidence at the α=.05 level of significance to conclude more than half of adults cannot eat just 1 m&m.

23 Hypothesis Test for Population Mean: P-Value Approach A local retailer claims that the mean waiting time is less than 9 minutes. A random sample of 0 waiting times has a mean of 7.4 minutes with a standard deviation of.1 minutes. At α = 0.01, test the retailer's claim. Assume the distribution is normally distributed. Test the retailer s claim using α=

24 Hypothesis Test for Population Mean 1) State the null and alternative hypothesis H o : μ = 9 H 1 : μ < 9 ) Find the t-value = = with 19 degrees of freedom 0 t = x μ 0 s n 3) Find the p-value (use the table or excel) P-value = ) Conclusion: Since the p-value is less than.01 (α), we reject the hypothesis. There is significant evidence that the mean waiting time is less than 9 minutes. 10.3

25 10.3 Hypothesis Test for Population Mean In 00, the mean age of inmate on death-row was 40.7 years. A researcher wonders if the mean age has changed since then. She randomly selects 3 death-row inmates and finds that their mean age is 38.9 with a standard deviation of 9.6. Test the researchers claim.

26 10.3 Hypothesis Test for Population Mean 1) State the Null and Alternative hypothesis h o : μ = 40.7 h 1 : μ 40.7 ) Calculate the test statistic t = x μ 0 s n = = 1.06 with 31 degrees of freedom 3) Find the p-value (use the table or excel) If using the table or a non tailed excel function, you need to divide the p-value by P-value =.970 We are not given a significance level (α), we use 5%. The p-value is greater than 5%, so we do not reject the null hypothesis. Conclusion: There is not sufficient evidence to reject the claim that the mean has changed.

27 10.4 Hypothesis Test for Population Standard Deviation A professor at an all-men's college determined that the standard deviation of men's heights is.5 inches. The professor then randomly selected 41 female students from a nearby allfemale college and found the standard deviation to be.9 inches. Test the professor's claim that the standard deviation of female heights is greater than.5 inches. Use α = 0.01.

28 Hypothesis Test for Population Standard Deviation 1. State the Null and Alternative hypothesis h o : σ =.5 h 1 : σ >.5. Calculate the test statistic χ 0 = (n 1)s = σ 0 (41 1).9.5 = Determine the P-value Look up value: Subtract from 1: = Conclusion: p-value> α (.01) Fail to reject the null hypothesis. There is not statistical evidence to support the claim that standard deviation is greater than

29 10.5 When to Use t and When to Use z Use Z Inference (confidence interval/ hypothesis testing) about population proportion Looking for sample sizes Have population standard deviation σ Use T Inference (confidence interval/ hypothesis testing) about population mean Sample standard deviation s (but not looking for sample size n)

30 Which Procedure to Use? 10.5

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

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

Stats Review Chapters 3-4

Stats Review Chapters 3-4 Stats Review Chapters 3-4 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

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

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

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

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

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

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

Online 12 - Sections 9.1 and 9.2-Doug Ensley

Online 12 - Sections 9.1 and 9.2-Doug Ensley Student: Date: Instructor: Doug Ensley Course: MAT117 01 Applied Statistics - Ensley Assignment: Online 12 - Sections 9.1 and 9.2 1. Does a P-value of 0.001 give strong evidence or not especially strong

More information

Stats Review Chapters 5-6

Stats Review Chapters 5-6 Stats Review Chapters 5-6 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

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

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

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 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

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

Math 108 Exam 3 Solutions Spring 00

Math 108 Exam 3 Solutions Spring 00 Math 108 Exam 3 Solutions Spring 00 1. An ecologist studying acid rain takes measurements of the ph in 12 randomly selected Adirondack lakes. The results are as follows: 3.0 6.5 5.0 4.2 5.5 4.7 3.4 6.8

More information

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%.

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%. Chapter 7-8 Exam Name: Answer the questions in the spaces provided. If you run out of room, show your work on a separate paper clearly numbered and attached to this exam. Please indicate which program

More information

Chapter 7 - Practice Problems 2

Chapter 7 - Practice Problems 2 Chapter 7 - Practice Problems 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the requested value. 1) A researcher for a car insurance company

More information

" Y. Notation and Equations for Regression Lecture 11/4. Notation:

 Y. Notation and Equations for Regression Lecture 11/4. Notation: Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through

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

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 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

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 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

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

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Ch. 10 Chi SquareTests and the F-Distribution 10.1 Goodness of Fit 1 Find Expected Frequencies Provide an appropriate response. 1) The frequency distribution shows the ages for a sample of 100 employees.

More 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

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

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

Lecture 42 Section 14.3. Tue, Apr 8, 2008

Lecture 42 Section 14.3. Tue, Apr 8, 2008 the Lecture 42 Section 14.3 Hampden-Sydney College Tue, Apr 8, 2008 Outline the 1 2 the 3 4 5 the The will compute χ 2 areas, but not χ 2 percentiles. (That s ok.) After performing the χ 2 test by hand,

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

Need for Sampling. Very large populations Destructive testing Continuous production process

Need for Sampling. Very large populations Destructive testing Continuous production process Chapter 4 Sampling and Estimation Need for Sampling Very large populations Destructive testing Continuous production process The objective of sampling is to draw a valid inference about a population. 4-

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

SAMPLE SIZE CONSIDERATIONS

SAMPLE SIZE CONSIDERATIONS SAMPLE SIZE CONSIDERATIONS Learning Objectives Understand the critical role having the right sample size has on an analysis or study. Know how to determine the correct sample size for a specific study.

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

Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)

Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1) Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the

More information

Hypothesis Testing Population Mean

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

More information

Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion

Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion Learning Objectives Upon successful completion of Chapter 8, you will be able to: Understand terms. State the null and alternative

More 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

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

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

Understand the role that hypothesis testing plays in an improvement project. Know how to perform a two sample hypothesis test.

Understand the role that hypothesis testing plays in an improvement project. Know how to perform a two sample hypothesis test. HYPOTHESIS TESTING Learning Objectives Understand the role that hypothesis testing plays in an improvement project. Know how to perform a two sample hypothesis test. Know how to perform a hypothesis test

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

Introduction to Hypothesis Testing

Introduction 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 information

Simple Linear Regression Inference

Simple Linear Regression Inference Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation

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

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

CHAPTER IV FINDINGS AND CONCURRENT DISCUSSIONS

CHAPTER IV FINDINGS AND CONCURRENT DISCUSSIONS CHAPTER IV FINDINGS AND CONCURRENT DISCUSSIONS Hypothesis 1: People are resistant to the technological change in the security system of the organization. Hypothesis 2: information hacked and misused. Lack

More information

Regression Analysis: A Complete Example

Regression Analysis: A Complete Example Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty

More information

Module 2 Probability and Statistics

Module 2 Probability and Statistics Module 2 Probability and Statistics BASIC CONCEPTS Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The standard deviation of a standard normal distribution

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

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

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

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

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

NPTEL STRUCTURAL RELIABILITY

NPTEL STRUCTURAL RELIABILITY NPTEL Course On STRUCTURAL RELIABILITY Module # 02 Lecture 6 Course Format: Web Instructor: Dr. Arunasis Chakraborty Department of Civil Engineering Indian Institute of Technology Guwahati 6. Lecture 06:

More information

Hypothesis Testing I

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),

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

CHAPTER 11 CHI-SQUARE: NON-PARAMETRIC COMPARISONS OF FREQUENCY

CHAPTER 11 CHI-SQUARE: NON-PARAMETRIC COMPARISONS OF FREQUENCY CHAPTER 11 CHI-SQUARE: NON-PARAMETRIC COMPARISONS OF FREQUENCY The hypothesis testing statistics detailed thus far in this text have all been designed to allow comparison of the means of two or more samples

More information

Odds ratio, Odds ratio test for independence, chi-squared statistic.

Odds ratio, Odds ratio test for independence, chi-squared statistic. Odds ratio, Odds ratio test for independence, chi-squared statistic. Announcements: Assignment 5 is live on webpage. Due Wed Aug 1 at 4:30pm. (9 days, 1 hour, 58.5 minutes ) Final exam is Aug 9. Review

More information

Review #2. Statistics

Review #2. Statistics Review #2 Statistics Find the mean of the given probability distribution. 1) x P(x) 0 0.19 1 0.37 2 0.16 3 0.26 4 0.02 A) 1.64 B) 1.45 C) 1.55 D) 1.74 2) The number of golf balls ordered by customers of

More 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

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

Chapter 7 TEST OF HYPOTHESIS

Chapter 7 TEST OF HYPOTHESIS Chapter 7 TEST OF HYPOTHESIS In a certain perspective, we can view hypothesis testing just like a jury in a court trial. In a jury trial, the null hypothesis is similar to the jury making a decision of

More information

Statistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice!

Statistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice! Statistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice!) Part A - Multiple Choice Indicate the best choice

More information

Having a coin come up heads or tails is a variable on a nominal scale. Heads is a different category from tails.

Having a coin come up heads or tails is a variable on a nominal scale. Heads is a different category from tails. Chi-square Goodness of Fit Test The chi-square test is designed to test differences whether one frequency is different from another frequency. The chi-square test is designed for use with data on a nominal

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 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

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

Is it statistically significant? The chi-square test

Is it statistically significant? The chi-square test UAS Conference Series 2013/14 Is it statistically significant? The chi-square test Dr Gosia Turner Student Data Management and Analysis 14 September 2010 Page 1 Why chi-square? Tests whether two categorical

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

Adverse Impact Ratio for Females (0/ 1) = 0 (5/ 17) = 0.2941 Adverse impact as defined by the 4/5ths rule was not found in the above data.

Adverse Impact Ratio for Females (0/ 1) = 0 (5/ 17) = 0.2941 Adverse impact as defined by the 4/5ths rule was not found in the above data. 1 of 9 12/8/2014 12:57 PM (an On-Line Internet based application) Instructions: Please fill out the information into the form below. Once you have entered your data below, you may select the types of analysis

More information

SPSS on two independent samples. Two sample test with proportions. Paired t-test (with more SPSS)

SPSS on two independent samples. Two sample test with proportions. Paired t-test (with more SPSS) SPSS on two independent samples. Two sample test with proportions. Paired t-test (with more SPSS) State of the course address: The Final exam is Aug 9, 3:30pm 6:30pm in B9201 in the Burnaby Campus. (One

More information

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

Unit 26 Estimation with Confidence Intervals

Unit 26 Estimation with Confidence Intervals Unit 26 Estimation with Confidence Intervals Objectives: To see how confidence intervals are used to estimate a population proportion, a population mean, a difference in population proportions, or a difference

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) ±1.88 B) ±1.645 C) ±1.96 D) ±2.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) ±1.88 B) ±1.645 C) ±1.96 D) ±2. Ch. 6 Confidence Intervals 6.1 Confidence Intervals for the Mean (Large Samples) 1 Find a Critical Value 1) Find the critical value zc that corresponds to a 94% confidence level. A) ±1.88 B) ±1.645 C)

More 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 Level I Quantitative Methods. IFT Notes for the CFA exam

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

More information

Independent t- Test (Comparing Two Means)

Independent t- Test (Comparing Two Means) Independent t- Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent t-test when to use the independent t-test the use of SPSS to complete an independent

More information

THE FIRST SET OF EXAMPLES USE SUMMARY DATA... EXAMPLE 7.2, PAGE 227 DESCRIBES A PROBLEM AND A HYPOTHESIS TEST IS PERFORMED IN EXAMPLE 7.

THE FIRST SET OF EXAMPLES USE SUMMARY DATA... EXAMPLE 7.2, PAGE 227 DESCRIBES A PROBLEM AND A HYPOTHESIS TEST IS PERFORMED IN EXAMPLE 7. THERE ARE TWO WAYS TO DO HYPOTHESIS TESTING WITH STATCRUNCH: WITH SUMMARY DATA (AS IN EXAMPLE 7.17, PAGE 236, IN ROSNER); WITH THE ORIGINAL DATA (AS IN EXAMPLE 8.5, PAGE 301 IN ROSNER THAT USES DATA FROM

More 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

Unit 29 Chi-Square Goodness-of-Fit Test

Unit 29 Chi-Square Goodness-of-Fit Test Unit 29 Chi-Square Goodness-of-Fit Test Objectives: To perform the chi-square hypothesis test concerning proportions corresponding to more than two categories of a qualitative variable To perform the Bonferroni

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

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a

More 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

Graphing calculators in teaching statistical p-values to elementary statistics students

Graphing calculators in teaching statistical p-values to elementary statistics students Graphing calculators in teaching statistical p-values to elementary statistics students ABSTRACT Eric Benson American University in Dubai The statistical output of interest to most elementary statistics

More information

COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES.

COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES. 277 CHAPTER VI COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES. This chapter contains a full discussion of customer loyalty comparisons between private and public insurance companies

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

Experimental Design. Power and Sample Size Determination. Proportions. Proportions. Confidence Interval for p. The Binomial Test

Experimental Design. Power and Sample Size Determination. Proportions. Proportions. Confidence Interval for p. The Binomial Test Experimental Design Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 To this point in the semester, we have largely

More information

Math 58. Rumbos Fall 2008 1. Solutions to Review Problems for Exam 2

Math 58. Rumbos Fall 2008 1. Solutions to Review Problems for Exam 2 Math 58. Rumbos Fall 2008 1 Solutions to Review Problems for Exam 2 1. For each of the following scenarios, determine whether the binomial distribution is the appropriate distribution for the random variable

More information

Two-sample hypothesis testing, II 9.07 3/16/2004

Two-sample hypothesis testing, II 9.07 3/16/2004 Two-sample hypothesis testing, II 9.07 3/16/004 Small sample tests for the difference between two independent means For two-sample tests of the difference in mean, things get a little confusing, here,

More information

Statistics Review PSY379

Statistics Review PSY379 Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses

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

Chapter 7. Section Introduction to Hypothesis Testing

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

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 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

Using Stata for Categorical Data Analysis

Using Stata for Categorical Data Analysis Using Stata for Categorical Data Analysis NOTE: These problems make extensive use of Nick Cox s tab_chi, which is actually a collection of routines, and Adrian Mander s ipf command. From within Stata,

More information

Chapter 23 Inferences About Means

Chapter 23 Inferences About Means Chapter 23 Inferences About Means Chapter 23 - Inferences About Means 391 Chapter 23 Solutions to Class Examples 1. See Class Example 1. 2. We want to know if the mean battery lifespan exceeds the 300-minute

More information

Two-Sample T-Tests Assuming Equal Variance (Enter Means)

Two-Sample T-Tests Assuming Equal Variance (Enter Means) Chapter 4 Two-Sample T-Tests Assuming Equal Variance (Enter Means) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when the variances of

More information

Lesson 1: Comparison of Population Means Part c: Comparison of Two- Means

Lesson 1: Comparison of Population Means Part c: Comparison of Two- Means Lesson : Comparison of Population Means Part c: Comparison of Two- Means Welcome to lesson c. This third lesson of lesson will discuss hypothesis testing for two independent means. Steps in Hypothesis

More information