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

Size: px
Start display at page:

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

Transcription

1 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 Problems Instructors: Dr. Samir Safi Mr. Ibrahim Abed SECTION I: MULTIPLE-CHOICE 1. The t test for the difference between the means of independent populations assumes that the respective a. sample sizes are equal. b. sample variances are equal. c. populations are approximately normal. d. All of the above.. If we are testing for the difference between the means of related populations with samples of n 1 = 0 and n = 0, the number of degrees of freedom is equal to a. 39. b. 38. c. 19. d In testing for differences between the means of two related populations, the null hypothesis is a. H 0 D =. b. H : 0 0 µ D =. c. H : 0 0 µ D <. d. H 0 D > In testing for differences between the means of two independent populations, the null hypothesis is: a. H 0: µ 1 µ =. b. H 0 1 µ = 0. c. H 0 1 µ > 0. d. H 0 1 µ <. 1

2 5. When testing H 0 1 µ 0 versus H 1 1 µ > 0, the observed value of the Z- score was found to be.13. The p-value for this test would be a b c d If we wish to determine whether there is evidence that the proportion of items of interest is higher in group 1 than in group, the appropriate test to use is a) the Z test for the difference between two proportions. b) the F test for the difference between two variances. c) the pooled-variance t test for the difference between two proportions. d) the F test for the difference between two proportions.

3 SECTION II: TRUE OR FALSE 1. The sample size in each independent sample must be the same if we are to test for differences between the means of independent populations. False. When testing for differences between the means of related populations, we can use either a one-tailed or two-tailed test. 3. The test for the equality of population variances assumes that each of the populations is normally distributed. 4. When the sample sizes are equal, the pooled variance of the groups is the average of the sample variances. 5. A researcher is curious about the effect of sleep on students test performances. He chooses 60 students and gives each tests: one given after hours sleep and one after 8 hours sleep. The test the researcher should use would be a related samples test. 6. A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with related samples. False 7. In testing the difference between two proportions using the normal distribution, we may use a two-tailed Z test. 3

4 SECTION III: FREE RESPONSE QUESTIONS TABLE (A) A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below. Hypothesized Difference 0 Level of Significance 0.05 Population 1 Sample Sample Size 18 Sample Mean Sample Standard Deviation Population Sample Sample Size 1 Sample Mean Sample Standard Deviation Difference in Sample Means t-test Statistic Lower-Tail Test Lower Critical Value p-value the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. According to the test run, which of the following is an appropriate alternative hypothesis? H > µ a. 1 females males b. H 1 females < µ males c. H 1 females µ males d. H 1 females = µ males. the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. From the analysis in Table 10-, the correct test statistic is: a b c d. 6,

5 3. the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. The proper conclusion for this test is: a. At the α = 0.10 level, there is sufficient evidence to indicate a difference in the mean starting salaries of male and female MBA graduates. b. At the α = 0.10 level, there is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates. c. At the α = 0.10 level, there is sufficient evidence to indicate that females have a higher mean starting salary than male MBA graduates. d. At the α = 0.10 level, there is insufficient evidence to indicate any difference in the mean starting salaries of male and female MBA graduates. 4. the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. What assumptions were necessary to conduct this hypothesis test? a. Both populations of salaries (male and female) must have approximate normal distributions. b. The population variances are approximately equal. c. The samples were randomly and independently selected. d. All of the above assumptions were necessary. 5. what is the 99% confidence interval estimate for the difference between two means? \$0, to \$6, what is the 95% confidence interval estimate for the difference between two means? \$ to \$3, what is the 90% confidence interval estimate for the difference between two means? \$14, to \$1, TABLE (B) To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. Exam Score Exam Score Student Before Course (1) After Course () ,

6 8. the number of degrees of freedom is a. 14. b. 13. c. 8. d the value of the sample mean difference is if the difference scores reflect the results of the exam after the course minus the results of the exam before the course. a. 0 b. 50 c. 68 d the value of the standard error of the difference scores is a b c..991 d what is the critical value for testing at the 5% level of significance whether the business school preparation course is effective in improving exam scores? a..365 b..145 c d at the 0.05 level of significance, the decision for this hypothesis test would be: e. reject the null hypothesis. f. do not reject the null hypothesis. g. reject the alternative hypothesis. h. It cannot be determined from the information given. 13. at the 0.05 level of significance, the conclusion for this hypothesis test would be: i. the business school preparation course does improve exam score. j. the business school preparation course does not improve exam score. k. the business school preparation course has no impact on exam score. l. It cannot be drawn from the information given. 14. the calculated value of the test statistic is the p-value of the test statistic is (using Excel) or between 0.05 and 0.05 (using Table E.3 with 7 degrees of freedom) 6

7 16. or False: in examining the differences between related samples we are essentially sampling from an underlying population of difference "scores." TABLE (C) To investigate the efficacy of a diet, a random sample of 16 male patients is drawn from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t-test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds. 1. the t test should be -tailed. one. the computed t statistic is there are degrees of freedom for this test the critical value for a one-tailed test of the null hypothesis of no difference at the α = 0.05 level of significance is a one-tailed test of the null hypothesis of no difference would (be rejected/not be rejected) at the α = 0.05 level of significance. be rejected 6. the p-value for a one-tailed test whose computed t statistic is.00 is between and if we were interested in testing against the two-tailed alternative that µ D is not equal to zero at the α = 0.05 level of significance, the null hypothesis would (be rejected/not be rejected). not be rejected 8. the p-value for a two-tailed test whose computed statistic is.00 is between and what is the 95% confidence interval estimate for the mean difference in weight before and after the diet? 0.0 to what is the 99% confidence interval estimate for the mean difference in weight before and after the diet? 1.4 to 7.4 7

8 11. what is the 90% confidence interval estimate for the mean difference in weight before and after the diet? 0.37 to 5.63 TABLE (D) A few years ago, Pepsi invited consumers to take the Pepsi Challenge. Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in determining what factors played a role in people s taste preferences. One of the factors studied was the gender of the consumer. Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi. Males: n = 109, p M = Females: n = 5, p F = 0.5 p M p F = Z = to determine if a difference exists in the taste preferences of men and women, give the correct alternative hypothesis that Pepsi would test. a) H 1 M µ F 0 b) H 1 M µ F > 0 c) H 1 : π M π F 0 d) H 1 : π M π F = 0. suppose Pepsi wanted to test to determine if the males preferred Pepsi more than the females. Using the test statistic given, compute the appropriate p-value for the test. a) b) c) d) suppose Pepsi wanted to test to determine if the males preferred Pepsi less than the females. Using the test statistic given, compute the appropriate p-value for the test. a) b) c) d) suppose that the two-tailed p-value was really State the proper conclusion. a) At α = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. b) At α = 0.10, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. c) At α = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi equals the proportion of females preferring Pepsi. d) At α = 0.08, there is insufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. 8

9 5. construct a 90% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi to construct a 95% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi. 0.0 to construct a 99% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi to 0.37 TABLE (E) A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π 1 and π represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. 1. if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses? a) H 0 : π 1 π = 0 versus H 1 : π 1 π 0 b) H 0 : π1 π 0 versus H 1 : π1 π = 0 c) H 0 : π1 π 0 versus H 1 : π1 π > 0 d) H 0 : π1 π 0 versus H 1 : π1 π < 0. if the firm wanted to test whether a greater proportion of workers would currently like to attend a self-improvement course than in the past, which represents the relevant hypotheses? a) H 0 : π1 π = 0 versus H 1 : π1 π 0 b) H 0 : π1 π 0 versus H 1 : π1 π = 0 c) H 0 : π1 π 0 versus H 1 : π1 π > 0 d) H 0 : π1 π 0 versus H 1 : π1 π < 0 3. what is the unbiased point estimate for the difference between the two population proportions? a) 0.06 b) 0.10 c) 0.15 d) what is/are the critical value(s) when performing a Z test on whether population proportions are different if α = 0.05? a) ± b) ±

10 c) 1.96 d) ± what is/are the critical value(s) when testing whether population proportions are different if α = 0.10? a) ± b) ± 1.96 c) d) ± what is/are the critical value(s) when testing whether the current population proportion is higher than before if α = 0.05? a) ± b) c) ± 1.96 d) what is the estimated standard error of the difference between the two sample proportions? a) 0.69 b) c) d) 0 8. what is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions? a) b) 1.96 c) d) 0 9. the company tests to determine at the 0.05 level whether the population proportion has changed from the previous study. Which of the following is most correct? a) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has changed over the intervening 10 years. b) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has not changed over the intervening 10 years. c) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years. d) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years. 10. construct a 99% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study. 10

11 0.08 to construct a 95% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study to construct a 90% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study to

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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: 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,

### 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 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

### Introduction to Analysis of Variance (ANOVA) Limitations of the t-test

Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One- Way ANOVA Limitations of the t-test Although the t-test is commonly used, it has limitations Can only

### 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

### Mind on Statistics. Chapter 13

Mind on Statistics Chapter 13 Sections 13.1-13.2 1. Which statement is not true about hypothesis tests? A. Hypothesis tests are only valid when the sample is representative of the population for the question

### 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

### 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

### Difference of Means and ANOVA Problems

Difference of Means and Problems Dr. Tom Ilvento FREC 408 Accounting Firm Study An accounting firm specializes in auditing the financial records of large firm It is interested in evaluating its fee structure,particularly

### 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,

### Introduction to. Hypothesis Testing CHAPTER LEARNING OBJECTIVES. 1 Identify the four steps of hypothesis testing.

Introduction to Hypothesis Testing CHAPTER 8 LEARNING OBJECTIVES After reading this chapter, you should be able to: 1 Identify the four steps of hypothesis testing. 2 Define null hypothesis, alternative

### 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

### 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

### 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.

### 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

### 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

### Introduction. Hypothesis Testing. Hypothesis Testing. Significance Testing

Introduction Hypothesis Testing Mark Lunt Arthritis Research UK Centre for Ecellence in Epidemiology University of Manchester 13/10/2015 We saw last week that we can never know the population parameters

### 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

### 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

### 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

### 22. HYPOTHESIS TESTING

22. HYPOTHESIS TESTING Often, we need to make decisions based on incomplete information. Do the data support some belief ( hypothesis ) about the value of a population parameter? Is OJ Simpson guilty?

### 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

### 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

### 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

### 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

### 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

### Good luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:

Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours

### t Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon

t-tests in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com www.excelmasterseries.com

### 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

### Opgaven Onderzoeksmethoden, Onderdeel Statistiek

Opgaven Onderzoeksmethoden, Onderdeel Statistiek 1. What is the measurement scale of the following variables? a Shoe size b Religion c Car brand d Score in a tennis game e Number of work hours per week

### Two-sample t-tests. - Independent samples - Pooled standard devation - The equal variance assumption

Two-sample t-tests. - Independent samples - Pooled standard devation - The equal variance assumption Last time, we used the mean of one sample to test against the hypothesis that the true mean was a particular

### 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.

### 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

### 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 =

### 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,

### 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.

### Mind on Statistics. Chapter 15

Mind on Statistics Chapter 15 Section 15.1 1. A student survey was done to study the relationship between class standing (freshman, sophomore, junior, or senior) and major subject (English, Biology, French,

### Chapter 26: Tests of Significance

Chapter 26: Tests of Significance Procedure: 1. State the null and alternative in words and in terms of a box model. 2. Find the test statistic: z = observed EV. SE 3. Calculate the P-value: The area under

### How To Test For Significance On A Data Set

Non-Parametric Univariate Tests: 1 Sample Sign Test 1 1 SAMPLE SIGN TEST A non-parametric equivalent of the 1 SAMPLE T-TEST. ASSUMPTIONS: Data is non-normally distributed, even after log transforming.

### Part 3. Comparing Groups. Chapter 7 Comparing Paired Groups 189. Chapter 8 Comparing Two Independent Groups 217

Part 3 Comparing Groups Chapter 7 Comparing Paired Groups 189 Chapter 8 Comparing Two Independent Groups 217 Chapter 9 Comparing More Than Two Groups 257 188 Elementary Statistics Using SAS Chapter 7 Comparing

### Calculating, Interpreting, and Reporting Estimates of Effect Size (Magnitude of an Effect or the Strength of a Relationship)

1 Calculating, Interpreting, and Reporting Estimates of Effect Size (Magnitude of an Effect or the Strength of a Relationship) I. Authors should report effect sizes in the manuscript and tables when reporting

### 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

### 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

### Comparing Two Groups. Standard Error of ȳ 1 ȳ 2. Setting. Two Independent Samples

Comparing Two Groups Chapter 7 describes two ways to compare two populations on the basis of independent samples: a confidence interval for the difference in population means and a hypothesis test. The

### 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.

### UNDERSTANDING THE INDEPENDENT-SAMPLES t TEST

UNDERSTANDING The independent-samples t test evaluates the difference between the means of two independent or unrelated groups. That is, we evaluate whether the means for two independent groups are significantly

### Unit 26: Small Sample Inference for One Mean

Unit 26: Small Sample Inference for One Mean Prerequisites Students need the background on confidence intervals and significance tests covered in Units 24 and 25. Additional Topic Coverage Additional coverage

### MONT 107N Understanding Randomness Solutions For Final Examination May 11, 2010

MONT 07N Understanding Randomness Solutions For Final Examination May, 00 Short Answer (a) (0) How are the EV and SE for the sum of n draws with replacement from a box computed? Solution: The EV is n times

### Statistiek II. John Nerbonne. October 1, 2010. Dept of Information Science j.nerbonne@rug.nl

Dept of Information Science j.nerbonne@rug.nl October 1, 2010 Course outline 1 One-way ANOVA. 2 Factorial ANOVA. 3 Repeated measures ANOVA. 4 Correlation and regression. 5 Multiple regression. 6 Logistic

### 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

### Study Guide for the Final Exam

Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make

### 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

### 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

### Two-Sample T-Tests Allowing Unequal Variance (Enter Difference)

Chapter 45 Two-Sample T-Tests Allowing Unequal Variance (Enter Difference) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when no assumption

### UNDERSTANDING THE DEPENDENT-SAMPLES t TEST

UNDERSTANDING THE DEPENDENT-SAMPLES t TEST A dependent-samples t test (a.k.a. matched or paired-samples, matched-pairs, samples, or subjects, simple repeated-measures or within-groups, or correlated groups)

### 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.

### 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

### 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

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

Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly

### Descriptive Statistics

Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

### Hypothesis Testing --- One Mean

Hypothesis Testing --- One Mean A hypothesis is simply a statement that something is true. Typically, there are two hypotheses in a hypothesis test: the null, and the alternative. Null Hypothesis The hypothesis

### Hypothesis Testing. Reminder of Inferential Statistics. Hypothesis Testing: Introduction

Hypothesis Testing PSY 360 Introduction to Statistics for the Behavioral Sciences Reminder of Inferential Statistics All inferential statistics have the following in common: Use of some descriptive statistic

### 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

### Confidence Intervals for the Difference Between Two Means

Chapter 47 Confidence Intervals for the Difference Between Two Means Introduction This procedure calculates the sample size necessary to achieve a specified distance from the difference in sample means

### 6.2 Normal distribution. Standard Normal Distribution:

6.2 Normal distribution Slide Heights of Adult Men and Women Slide 2 Area= Mean = µ Standard Deviation = σ Donation: X ~ N(µ,σ 2 ) Standard Normal Distribution: Slide 3 Slide 4 a normal probability distribution

### 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

### Pearson's Correlation Tests

Chapter 800 Pearson's Correlation Tests Introduction The correlation coefficient, ρ (rho), is a popular statistic for describing the strength of the relationship between two variables. The correlation

### NONPARAMETRIC STATISTICS 1. depend on assumptions about the underlying distribution of the data (or on the Central Limit Theorem)

NONPARAMETRIC STATISTICS 1 PREVIOUSLY parametric statistics in estimation and hypothesis testing... construction of confidence intervals computing of p-values classical significance testing depend on assumptions

### In the past, the increase in the price of gasoline could be attributed to major national or global

Chapter 7 Testing Hypotheses Chapter Learning Objectives Understanding the assumptions of statistical hypothesis testing Defining and applying the components in hypothesis testing: the research and null

### STAT 350 Practice Final Exam Solution (Spring 2015)

PART 1: Multiple Choice Questions: 1) A study was conducted to compare five different training programs for improving endurance. Forty subjects were randomly divided into five groups of eight subjects

### SURVEY OF STUDENTS FAMILIARITY WITH GRAMMAR AND MECHANICS OF ENGLISH LANGUAGE AN EXPLORATORY ANALYSIS. Hialeah, FL 33012, USA. Email: mshakil@mdc.

Polygon Spring 2010 Vol. 4, 43-55 SURVEY OF STUDENTS FAMILIARITY WITH GRAMMAR AND MECHANICS OF ENGLISH LANGUAGE AN EXPLORATORY ANALYSIS M. Shakil 1, V. Calderin 2 and L. Pierre-Philippe 3 1 Department

### Chapter Study Guide. Chapter 11 Confidence Intervals and Hypothesis Testing for Means

OPRE504 Chapter Study Guide Chapter 11 Confidence Intervals and Hypothesis Testing for Means I. Calculate Probability for A Sample Mean When Population σ Is Known 1. First of all, we need to find out the

### 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,

### SCHOOL OF HEALTH AND HUMAN SCIENCES DON T FORGET TO RECODE YOUR MISSING VALUES

SCHOOL OF HEALTH AND HUMAN SCIENCES Using SPSS Topics addressed today: 1. Differences between groups 2. Graphing Use the s4data.sav file for the first part of this session. DON T FORGET TO RECODE YOUR

### A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

CHAPTER 5. A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING 5.1 Concepts When a number of animals or plots are exposed to a certain treatment, we usually estimate the effect of the treatment

### 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

### Section Format Day Begin End Building Rm# Instructor. 001 Lecture Tue 6:45 PM 8:40 PM Silver 401 Ballerini

NEW YORK UNIVERSITY ROBERT F. WAGNER GRADUATE SCHOOL OF PUBLIC SERVICE Course Syllabus Spring 2016 Statistical Methods for Public, Nonprofit, and Health Management Section Format Day Begin End Building

### 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

### Impact of Enrollment Timing on Performance: The Case of Students Studying the First Course in Accounting

Journal of Accounting, Finance and Economics Vol. 5. No. 1. September 2015. Pp. 1 9 Impact of Enrollment Timing on Performance: The Case of Students Studying the First Course in Accounting JEL Code: M41

### KSTAT MINI-MANUAL. Decision Sciences 434 Kellogg Graduate School of Management

KSTAT MINI-MANUAL Decision Sciences 434 Kellogg Graduate School of Management Kstat is a set of macros added to Excel and it will enable you to do the statistics required for this course very easily. To

### Chapter 7 Section 7.1: Inference for the Mean of a Population

Chapter 7 Section 7.1: Inference for the Mean of a Population Now let s look at a similar situation Take an SRS of size n Normal Population : N(, ). Both and are unknown parameters. Unlike what we used

### 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

### 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

### Tests of Hypotheses Using Statistics

Tests of Hypotheses Using Statistics Adam Massey and Steven J. Miller Mathematics Department Brown University Providence, RI 0292 Abstract We present the various methods of hypothesis testing that one

### 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

### CHAPTER 13. Experimental Design and Analysis of Variance

CHAPTER 13 Experimental Design and Analysis of Variance CONTENTS STATISTICS IN PRACTICE: BURKE MARKETING SERVICES, INC. 13.1 AN INTRODUCTION TO EXPERIMENTAL DESIGN AND ANALYSIS OF VARIANCE Data Collection

### STATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4

STATISTICS 8, FINAL EXAM NAME: KEY Seat Number: Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 Make sure you have 8 pages. You will be provided with a table as well, as a separate

### 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

### Chapter 9. Two-Sample Tests. Effect Sizes and Power Paired t Test Calculation

Chapter 9 Two-Sample Tests Paired t Test (Correlated Groups t Test) Effect Sizes and Power Paired t Test Calculation Summary Independent t Test Chapter 9 Homework Power and Two-Sample Tests: Paired Versus