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

Save this PDF as:

Size: px
Start display at page:

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

## Transcription

1 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 null hypothesis is false. b. a correct decision when the null hypothesis is true. c. an incorrect decision when the null hypothesis is false. d. an incorrect decision when the null hypothesis is true. 2. The hypothesis of most interest to the researcher is: a. the alternative hypothesis. b. the null hypothesis. c. both hypotheses are of equal interest. d. Neither hypothesis is of interest. 3. A Type I error occurs when we: a. reject a false null hypothesis. b. reject a true null hypothesis. c. don't reject a false null hypothesis. d. don't reject a true null hypothesis. 4. A Type II error is defined as: a. rejecting a true null hypothesis. b. rejecting a false null hypothesis. c. not rejecting a true null hypothesis. d. not rejecting a false null hypothesis. 5. The probability of a Type II error is denoted by: a. α b. β c. 1 α d. 1 β 6. Which of the following would be an appropriate alternative hypothesis? a. The mean of a population is equal to 70. b. The mean of a sample is equal to 70. c. The mean of a population is greater than 70. d. The mean of a sample is greater than Suppose we wish to test H 0 : µ = 45 vs. H 1 : µ > 45. What will result if we conclude that the mean is greater than 45 when the actual mean is 50? a. We have made a Type I error. b. We have made a Type II error. c. We have made both a Type I error and a Type II error. d. We have made the correct decision. 1

2 Name: 8. Researchers claim that 60 tissues is the average number of tissues a person uses during the course of a cold. The company who makes Kleenex brand tissues thinks that fewer of their tissues are needed. What are their null and alternative hypotheses? a. H 0 : µ = 60 vs. H 1 : µ > 60 b. H 0 : µ = 60 vs. H 1 : µ < 60 c. H 0 : X = 60 vs. H 1 : X < 60 d. H 0 : µ < 60 vs. H 1 : µ = Which of the following p-values will lead us to reject the null hypothesis if the level of significance equals 0.05? a b c d Suppose that we reject a null hypothesis at the 0.05 level of significance. Then for which of the following α-values do we also reject the null hypothesis? a b c d In a two-tail test for the population mean, if the null hypothesis is rejected when the alternative hypothesis is true: a. a Type I error is committed. b. a Type II error is committed. c. a correct decision is made. d. a one-tail test should be used instead of a two-tail test. 12. Using a confidence interval when conducting a two-tail test for µ, we do not reject H 0 if the hypothesized value for µ: a. is to the left of the lower confidence limit (LCL). b. is to the right of the upper confidence limit (UCL). c. falls between the LCL and UCL. d. falls in the rejection region. 13. In testing the hypothesis H 0 : µ = 100 vs. H 1 : µ > 100, the p-value is found to be 0.074, and the sample mean is 105. Which of the following statements is true? a. The probability of observing a sample mean at least as large as 105 from a population whose mean is 100 is b. The probability of observing a sample mean smaller than 105 from a population whose mean is 100 is c. The probability that the population mean is larger than 100 is d. None of these choices. 2

3 Name: 14. The p-value of a test is the: a. smallest α at which the null hypothesis can be rejected. b. largest α at which the null hypothesis can be rejected. c. smallest α at which the null hypothesis cannot be rejected. d. largest α at which the null hypothesis cannot be rejected. 15. We have created a 95% confidence interval for µ with the results (10, 25). What conclusion will we make if we test H 0 : µ = 26 vs. H 1 : µ 26 at α = 0.025? a. Reject H 0 in favor of H 1 b. Accept H 0 in favor of H 1 c. Fail to reject H 0 in favor of H 1 d. We cannot tell from the information given. 16. The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club. She would now like to determine whether or not the mean age of her customers is over 35. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 35.5 years and the population standard deviation was 5 years. What is the p-value associated with the test statistic? a b c d The numerical quantity computed from the data that is used in deciding whether to reject H 0 is the: a. significance level. b. critical value. c. test statistic. d. parameter. 18. The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club. She would now like to determine whether or not the mean age of her customers is over 35. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. If she wants to be 99% confident in her decision, what rejection region she use if the population standard deviation σ is known? a. Reject H 0 if z < 2.33 b. Reject H 0 if z < 2.58 c. Reject H 0 if z > 2.33 d. Reject H 0 if z > For a given level of significance, if the sample size increases, the probability of a Type II error will: a. remain the same. b. increase. c. decrease. d. be equal to 1.0 regardless of α. 3

4 Name: 20. The power of a test is measured by its capability of: a. rejecting a null hypothesis that is true. b. not rejecting a null hypothesis that is true. c. rejecting a null hypothesis that is false. d. not rejecting a null hypothesis that is false. 21. If the probability of committing a Type I error for a given test is decreased, then for a fixed sample size n, the probability of committing a Type II error will: a. decrease. b. increase. c. stay the same. d. Not enough information to tell. 22. The power of a test is denoted by: a. α b. β c. 1 α d. 1 β 23. For a given level of significance α, if the sample size n is increased, the probability of a Type II error β will: a. decrease. b. increase. c. remain the same. d. Not enough information to tell. 24. For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t-distribution equal n 1 because we lose one degree of freedom by using the: a. sample mean as an estimate of the population mean. b. sample standard deviation as an estimate of the population standard deviation. c. sample proportion as an estimate of the population proportion. d. sample size as an estimate of the population size. 25. A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: x = \$50.50 and s 2 = 400. A 95% confidence interval for the average amount the credit card customers spent on their first visit to the chain's new store in the mall is: a. \$50.50 ± \$9.09. b. \$50.50 ± \$ c. \$50.50 ± \$ d. None of these choices. 26. Under what condition(s) does the test statistic for p have an approximate normal distribution? a. When np > 5. b. When np and np(1 p) are both > 5. c. When n > 30. d. When np and n(1 p) are both > 5. 4

5 Name: 27. After calculating the sample size needed to estimate a population proportion to within 0.04, your statistics professor told you the maximum allowable error must be reduced to just.01. If the original calculation led to a sample size of 800, the sample size will now have to be: a. 800 b c. 12,800 d The width of a confidence interval estimate for a proportion will be: a. narrower for 99% confidence than for 95% confidence. b. wider for a sample size of 100 than for a sample size of 50. c. narrower for 90% confidence than for 95% confidence. d. narrower when the sample proportion if 0.50 than when the sample proportion is True/False Indicate whether the statement is true or false. 29. There is an inverse relationship between the probabilities of Type I and Type II errors; as one increases, the other decreases, and vice versa. 30. For a given level of significance, if the sample size is increased, the probability of committing a Type II error will decrease. 31. The critical values will bound the rejection and non-rejection regions for the null hypothesis. 32. A one-tail test for the population mean µ produces a test-statistic z = The p-value associated with the test is For a given level of significance, if the sample size is increased, the probability of committing a Type I error will decrease. 34. The power of the test refers to the probability of rejecting a false null hypothesis. 35. As the alternative value of µ increases, so does the power of the test. 36. The statistic (x µ) / (s / of freedom. n ) when the sampled population is normal is Student t-distributed with n degrees 37. The lower limit of the 90% confidence interval for the population proportion p, given that n = 400 and p8 = 0.10, is In determining the sample size needed to estimate the population proportion p, we let the sample proportion p8 = 1 if we have no knowledge of even the approximate values of p8. 5

6 Name: Short Answer 39. Suppose a delivery company states that their packages arrive within two days or less on average. You want to find out whether the actual average delivery time is longer than this. You conduct a hypothesis test. a. Set up the null and alternative hypotheses. b. Suppose you conclude wrongly that the company's statement about average delivery time is within two days. What type of error is being committed and what is the impact of that error? c. Suppose you conclude wrongly that the delivery company's average time to delivery is in fact longer than two days. What type of error did you commit and what is the impact of this error? d. Which error is worse from the company's standpoint, a Type I or a Type II error? Why? e. Which error is worse from a consumer standpoint, a Type I or a Type II error? Why? GRE Scores The Admissions officer for the graduate programs at Michigan State University (MSU) believes that the average score on the GRE exam at his university is significantly higher than the national average of 1,300. An accepted standard deviation for GRE scores is 125. A random sample of 25 scores had an average of 1, {GRE Scores Narrative} Calculate the value of the test statistic and set up the rejection region at the level. What is your conclusion? 41. {GRE Scores Narrative} Calculate the p-value. Grocery Receipts A simple random sample of 100 grocery receipts was drawn from a normal population. The mean and standard deviation of the sample were \$120 and \$25, respectively. 42. {Grocery Receipts Narrative} Test the hypothesis H 0 : µ = 125 vs. H 1 : µ 125 at the 10% significance level. 43. A drug company has just developed a new pill to alleviate the symptoms of allergies and colds. However, they are concerned about the variability in the amount of time until the drug becomes effective. In a random sample of 10 individuals who suffer from allergies, the amount of time (in hours) for the pill to take effect was recorded and listed as follows: 5, 7, 6, 10, 9, 12, 8, 17, 4, and 16. Estimate with 90% confidence the variance of the time for the drug to become effective. Independent Voters A pollster wants to challenge a claim that 5% of the registered voters in her state are Independent; she thinks the percentage is lower than that. In a test of hypothesis, H 0 : p = 0.05 vs. H 1 : p < 0.05, her random sample of size 1,000 registered voters revealed that the number of Independents was {Independent Voters Narrative} Compute the p-value and explain how to use it to test the hypotheses. 6

7 Name: Union Contract A union composed of several thousand employees is preparing to vote on a new contract. A random sample of 500 employees yielded 320 who planned to vote yes. It is believed that the new contract will receive more than 60% yes votes. 45. {Union Contract Narrative} Compute the p-value for the test. New Product After a financial analysis, the general manager of a large company decided that if more than 8% of potential buyers of a new product purchase that product, the company would show a profit. In a preliminary survey of 500 potential buyers, 56 people say that they will buy the product. 46. {New Product Narrative} Is there sufficient evidence at the 5% significance level that the product will produce a profit? Allergy Drug A company claims that 10% of the users of a certain allergy drug experience drowsiness. In clinical studies of this allergy drug, 81 of the 900 subjects experienced drowsiness 47. {Allergy Drug Narrative} Is there enough evidence at the 5% significance level to infer that the competitor is correct? Car Dealership An accountant was performing an audit for a car dealership. An auditor wants to examine the monetary error made by the purchasing order department in the month of July. He decided to randomly sample 100 of the 925 purchase orders for the month of July, and found the amount of error in each one. The statistics for this sample were: x = \$6.0 and s = \$ {Car Dealership Narrative} Estimate with 95% confidence the average amount of error per purchase order for the entire month of July. 7

8 HypoTesting Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 REF: SECTION ANS: A PTS: 1 REF: SECTION ANS: B PTS: 1 REF: SECTION ANS: D PTS: 1 REF: SECTION ANS: B PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: D PTS: 1 REF: SECTION ANS: B PTS: 1 REF: SECTION ANS: D PTS: 1 REF: SECTION ANS: A PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: A PTS: 1 REF: SECTION ANS: A PTS: 1 REF: SECTION ANS: D PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: B PTS: 1 REF: SECTION ANS: D PTS: 1 REF: SECTION ANS: A PTS: 1 REF: SECTION ANS: A PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: D PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION 12.3 TRUE/FALSE 29. ANS: T PTS: 1 REF: SECTION ANS: T PTS: 1 REF: SECTION ANS: T PTS: 1 REF: SECTION ANS: F PTS: 1 REF: SECTION ANS: F PTS: 1 REF: SECTION ANS: T PTS: 1 REF: SECTION ANS: T PTS: 1 REF: SECTION ANS: F PTS: 1 REF: SECTION

9 37. ANS: F PTS: 1 REF: SECTION ANS: F PTS: 1 REF: SECTION 12.3 SHORT ANSWER 39. ANS: a. H 0 : µ = 2 days vs. H 1 : µ > 2 days b. You did not reject the company's claim but you should have. This is a Type II error. It is a missed opportunity to say the company's claim is wrong. The impact is that people will not get their packages delivered within 2 days on average, and could eventually become dissatisfied. c. You rejected the company's claim but you should not have. This is a Type I error. You caused a false alarm. The impact is that the company loses its credibility needlessly. This could cause some real problems for the person who made the false alarm. d. The company does not want to lose its reputation unfairly, so they want to minimize the chance for a Type I error. However, this increases the chance that customers will get their packages delivered later than promised, on average. e. The consumer wants to know their packages are being delivered as promised (on average), so they want to decrease the chance of a Type II error. However, this increases the chance of a false alarm. PTS: 1 REF: SECTION ANS: Test statistic: z = 3.0 Rejection region: z > z.025 = 1.96 Conclusion: Reject H 0. There is enough statistical evidence to infer that the average GRE for all graduate students at MSU is higher than 1,300. PTS: 1 REF: SECTION ANS: p-value = PTS: 1 REF: SECTION ANS: Rejection region: t > t 0.05,99 = 1.66 Test statistic: t = 2.0 Conclusion: Reject H 0. We can infer that the population mean is not equal to 125. According to our data, the mean is lower than that. PTS: 1 REF: SECTION

10 43. ANS: LCL = (n 1)s 2 2 / χ 0.05,9 = UCL = (n 1)s 2 2 / χ 0.95,9 = We estimate that the variance of the time for the drug to become effective lies between and PTS: 1 REF: SECTION ANS: p-value = Since p-value = > α = 0.05, don't reject H 0. PTS: 1 REF: SECTION ANS: p-value = PTS: 1 REF: SECTION ANS: Rejection region: z > z 0.05 = Test statistic: z = Conclusion: Reject H 0. Yes, there is sufficient evidence at the 5% significance level that the product will produce a profit. PTS: 1 REF: SECTION ANS: Rejection region: z > z = 1.96 Test statistic: z = 1.0 Conclusion: Don't reject H 0. Not enough evidence at the 5% significance level to infer that the company is incorrect. PTS: 1 REF: SECTION ANS: s N n x ± t α / 2 = 6.0 ± = 6.0 ± n N LCL = \$2.81, and UCL = \$9.19 error per purchase order. PTS: 1 REF: SECTION

### 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 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

### 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

### Practice Problems and Exams

Practice Problems and Exams 1 The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 1302) Spring Semester 2009-2010

### 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

### 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.

### 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

### 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

### 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

### 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

### 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 AND TYPE I AND TYPE II ERROR

HYPOTHESIS TESTING AND TYPE I AND TYPE II ERROR Hypothesis is a conjecture (an inferring) about one or more population parameters. Null Hypothesis (H 0 ) is a statement of no difference or no relationship

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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 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

### 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,

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

STT315 Practice Ch 5-7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The length of time a traffic signal stays green (nicknamed

### 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

### 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,

### 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 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

### 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

### 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

About Hypothesis Testing TABLE OF CONTENTS About Hypothesis Testing... 1 What is a HYPOTHESIS TEST?... 1 Hypothesis Testing... 1 Hypothesis Testing... 1 Steps in Hypothesis Testing... 2 Steps in Hypothesis

### 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

### 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

### 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

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

Class: Date: Regression Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given the least squares regression line y8 = 5 2x: a. the relationship between

### 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

### 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

### 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

### Two-sample hypothesis testing, I 9.07 3/09/2004

Two-sample hypothesis testing, I 9.07 3/09/2004 But first, from last time More on the tradeoff between Type I and Type II errors The null and the alternative: Sampling distribution of the mean, m, given

### 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

### 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

### Module 5 Hypotheses Tests: Comparing Two Groups

Module 5 Hypotheses Tests: Comparing Two Groups Objective: In medical research, we often compare the outcomes between two groups of patients, namely exposed and unexposed groups. At the completion of this

### 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

### Psychology 60 Fall 2013 Practice Exam Actual Exam: Next Monday. Good luck!

Psychology 60 Fall 2013 Practice Exam Actual Exam: Next Monday. Good luck! Name: 1. The basic idea behind hypothesis testing: A. is important only if you want to compare two populations. B. depends on

### 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

### 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

### 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

### 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

### 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

### Hypothesis Testing. Hypothesis Testing CS 700

Hypothesis Testing CS 700 1 Hypothesis Testing! Purpose: make inferences about a population parameter by analyzing differences between observed sample statistics and the results one expects to obtain if

### 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

### 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

### Chapter 7 Part 2. Hypothesis testing Power

Chapter 7 Part 2 Hypothesis testing Power November 6, 2008 All of the normal curves in this handout are sampling distributions Goal: To understand the process of hypothesis testing and the relationship

### 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,

### Hypothesis Testing. Hypothesis Testing

Hypothesis Testing Daniel A. Menascé Department of Computer Science George Mason University 1 Hypothesis Testing Purpose: make inferences about a population parameter by analyzing differences between observed

### Estimation of σ 2, the variance of ɛ

Estimation of σ 2, the variance of ɛ The variance of the errors σ 2 indicates how much observations deviate from the fitted surface. If σ 2 is small, parameters β 0, β 1,..., β k will be reliably estimated

### 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

### 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

### Hypothesis testing S2

Basic medical statistics for clinical and experimental research Hypothesis testing S2 Katarzyna Jóźwiak k.jozwiak@nki.nl 2nd November 2015 1/43 Introduction Point estimation: use a sample statistic to

### Hypothesis testing - Steps

Hypothesis testing - Steps Steps to do a two-tailed test of the hypothesis that β 1 0: 1. Set up the hypotheses: H 0 : β 1 = 0 H a : β 1 0. 2. Compute the test statistic: t = b 1 0 Std. error of b 1 =

### [Chapter 10. Hypothesis Testing]

[Chapter 10. Hypothesis Testing] 10.1 Introduction 10.2 Elements of a Statistical Test 10.3 Common Large-Sample Tests 10.4 Calculating Type II Error Probabilities and Finding the Sample Size for Z Tests

### Chapter 11-12 1 Review

Chapter 11-12 Review Name 1. In formulating hypotheses for a statistical test of significance, the null hypothesis is often a statement of no effect or no difference. the probability of observing the data

### 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

### General Procedure for Hypothesis Test. Five types of statistical analysis. 1. Formulate H 1 and H 0. General Procedure for Hypothesis Test

Five types of statistical analysis General Procedure for Hypothesis Test Descriptive Inferential Differences Associative Predictive What are the characteristics of the respondents? What are the characteristics

### Mind on Statistics. Chapter 12

Mind on Statistics Chapter 12 Sections 12.1 Questions 1 to 6: For each statement, determine if the statement is a typical null hypothesis (H 0 ) or alternative hypothesis (H a ). 1. There is no difference

### 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

### Statistical Inference

Statistical Inference Idea: Estimate parameters of the population distribution using data. How: Use the sampling distribution of sample statistics and methods based on what would happen if we used this

### 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

### 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

### Multiple random variables

Multiple random variables Multiple random variables We essentially always consider multiple random variables at once. The key concepts: Joint, conditional and marginal distributions, and independence of

### 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

### 9_1&9_2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

9_1&9_2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Express the null hypothesis. 1) Which could be the null hypothesis for the true proportion

### 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

### Chapter 08. Introduction

Chapter 08 Introduction Hypothesis testing may best be summarized as a decision making process in which one attempts to arrive at a particular conclusion based upon "statistical" evidence. A typical hypothesis

### 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

### 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

### WISE Power Tutorial All Exercises

ame Date Class WISE Power Tutorial All Exercises Power: The B.E.A.. Mnemonic Four interrelated features of power can be summarized using BEA B Beta Error (Power = 1 Beta Error): Beta error (or Type II

### Hypothesis Testing. Barrow, Statistics for Economics, Accounting and Business Studies, 4 th edition Pearson Education Limited 2006

Hypothesis Testing Lecture 4 Hypothesis Testing Hypothesis testing is about making decisions Is a hypothesis true or false? Are women paid less, on average, than men? Principles of Hypothesis Testing The

### 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

### Chapter 2: Data quantifiers: sample mean, sample variance, sample standard deviation Quartiles, percentiles, median, interquartile range Dot diagrams

Review for Final Chapter 2: Data quantifiers: sample mean, sample variance, sample standard deviation Quartiles, percentiles, median, interquartile range Dot diagrams Histogram Boxplots Chapter 3: Set

### HYPOTHESIS TESTING III: POPULATION PROPORTIONS, ETC.

HYPOTHESIS TESTING III: POPULATION PROPORTIONS, ETC. HYPOTHESIS TESTS OF POPULATION PROPORTIONS Purpose: to determine whether the proportion in the population with some characteristic is or is not equal

### 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

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

Sample Practice problems - chapter 12-1 and 2 proportions for inference - Z Distributions Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide

### 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

### 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

### 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

### p ˆ (sample mean and sample

Chapter 6: Confidence Intervals and Hypothesis Testing When analyzing data, we can t just accept the sample mean or sample proportion as the official mean or proportion. When we estimate the statistics

### Introduction to Hypothesis Testing OPRE 6301

Introduction to Hypothesis Testing OPRE 6301 Motivation... The purpose of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief, or hypothesis, about

### 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.............................

### 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

### Hypothesis Testing Summary

Hypothesis Testing Summary Hypothesis testing begins with the drawing of a sample and calculating its characteristics (aka, statistics ). A statistical test (a specific form of a hypothesis test) is an

### 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

### 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.

### Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS

Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS Choose the single best answer for each question. Discuss questions with classmates, TAs and Professor Whitten. Raise your hand to check

### Simple Regression Theory II 2010 Samuel L. Baker

SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the

### 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

### 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

### 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

### 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