Introduction to Hypothesis Testing. Copyright 2014 Pearson Education, Inc. 9-1

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Introduction to Hypothesis Testing. Copyright 2014 Pearson Education, Inc. 9-1"

Transcription

1 Introduction to Hypothesis Testing 9-1

2 Learning Outcomes Outcome 1. Formulate null and alternative hypotheses for applications involving a single population mean or proportion. Outcome 2. Know what Type I and Type II errors are. Outcome 3. Correctly formulate a decision rule for testing a hypothesis. Outcome 4. Know how to use the test statistic, critical value, and p-value approaches to test a hypothesis. Outcome 5. Compute the probability of a Type II error. 9-2

3 9.1 Hypothesis Tests for Means Hypothesis Testing is an application of statistical inference Is performed in many industries Is a major part of business statistics Provides managers with a structured analytical method for making decisions about population means, proportions, as well as comparing different populations 9-3

4 Formulating the Hypotheses Null Hypothesis The statement about the population parameter that will be assumed to be true during the conduct of the hypothesis test The null hypothesis will be rejected only if the sample data provide substantial contradictory evidence Alternative Hypothesis The hypothesis that includes all population values not included in the null hypothesis 9-4

5 Formulating Hypothesis - Examples Testing the Status Quo The box of cereal has a mean fill of 16 ounces Testing a Research Hypothesis Goodyear s tire will last longer than its competitor s, or more than 60,000 miles Testing a Claim about Population Average waiting time in a medical clinic is less than 15 minutes 9-5

6 Formulating the Null and Alternative Hypothesis 9-6

7 Types of Statistical Errors Statistical Errors Type I Error No Error Type II Error Rejecting the null hypothesis when it is, in fact, true Failing to reject the null hypothesis when it is, in fact, false 9-7

8 Significance Level and Critical Value 9-8

9 Significance Level and Critical Value 9-9

10 Type I and II Errors Relationship Type I and Type II errors cannot happen at the same time Type I error can only occur if H 0 is true Type II error can only occur if H 0 is false If Type I error probability ( ) decreases, then Type II error probability (β) increases 9-10

11 9-11

12 Decision Rules and Test Statistics Approaches to Conduct the Hypothesis Test Test Statistic: A function of the sampled observations that provides a basis for testing a statistical hypothesis. 9-12

13 One-Tailed Test: A hypothesis test in which the entire rejection region is located in one tail of the sampling distribution Two-Tailed Test: A hypothesis test in which the entire rejection region is split into two tails of the sampling distribution 9-13

14 Types of Hypothesis Tests Variations in Hypothesis Testing 9-14

15 9-15

16 Recently, research physicians have developed a knee-replacement surgery process they believe will reduce the average patient recovery time. The hospital board will not recommend the new procedure unless there is substantial evidence to suggest that it is better than the existing procedure. The current mean recovery rate for the standard procedure is 142 days, with a standard deviation of 15 days. 9-16

17 Construct the rejection region Compute test statistic: Reach a decision: Draw a conclusion: Do not reject the null hypothesis There is not sufficient evidence to conclude that the new knee replacement procedure results in a shorter average recovery period

18 x ( /2)L x ( /2)U x ( /2)L x ( /2)U 9-18

19 9-19

20 Construct the rejection region Compute test statistic: Reach a decision: Draw a conclusion: Do not reject the null hypothesis There is not sufficient evidence to reject the null hypothesis

21 p-value Approach p-value: The probability (assuming the null hypothesis is true) of obtaining a test statistic at least as extreme as the test statistic we calculated from the sample. The p-value is also known as the observed significance level. If p-value <, reject H 0 If p-value, do not reject H

22 p-value Approach Adds a degree of significance to the result of the hypothesis test More than just a simple reject Can now determine how strongly you reject or accept The farther the p-value is from, the stronger the decision 9-22

23 Using p-values to Test a Null Hypothesis - Example Company packages salted and unsalted peanuts in 16-ounce sacks. The company s filling process strives for an average fill amount equal to 16 ounces. Using Excel: Because it is two-tailed hypothesis test: Draw a conclusion: 9-23

24 t-test Statistic: To employ the t-distribution, the following assumption needs to be made: The population is normally distributed 9-24

25 9-25

26 9-26

27 A tire company conducted a test on a new tire design to determine whether the company could make the claim that the mean tire mileage would exceed 60,000 miles. A simple random sample of 100 tires was tested, and the number of miles each tire lasted was recorded. Compute test statistic: Draw a conclusion: 9-27

28 9.2 Hypothesis Tests for a Proportion 9-28

29 Hypothesis Tests for a Proportion Involves categorical values Two possible outcomes Success (possesses a certain characteristic) Failure (does not possesses that characteristic) Examples: Scored shots to the basket per game Defective items manufactured 9-29

30 Hypothesis Tests for a Proportion z ( / 2)L z ( / 2)U p ( / 2)L p ( / 2)U 9-30

31 Hypothesis Tests for a Proportion 9-31

32 Hypothesis Test for a Population Proportion - Example A League is considering increasing the season ticket prices for basketball games. The marketing manager is concerned that some people will terminate their ticket orders if this change occurs. If more than 10% of the season ticket orders would be terminated, the marketing manager does not want to implement the price increase 9-32

33 Estimation and Hypothesis Testing for Two Populations Parameters 10-1

34 Learning Outcomes Outcome 1. Discuss the logic behind and demonstrate the techniques for using impendent samples to test hypotheses and develop interval estimates for the difference between two popular means. Outcome 2. Develop confidence interval estimates and conduct hypothesis tests for the difference between two population means for paired samples Outcome 3. Carry out hypothesis tests and establish interval estimates, using sample data, for the difference between two population proportions

35 10.1 Estimation for Two Population Means Using Independent Samples Independent Samples Samples selected from two or more populations in such a way that the occurrence of values in one sample has no influence on the probability of the occurrence of values in the other sample(s). Estimation for Two Population Means The population standard deviations are known The population standard deviations are unknown 10-35

36 - Variance of population 1 - Variance of population 2 n 1 and n 2 - Sample sizes from populations 1 and

37 z-values for several of the most used confidence levels: 10-37

38 Step 1: Define the population parameter of interest and select independent samples from the two populations Step 2: Specify the desired confidence level Step 3: Compute the point estimate Step 4: Determine the standard error of the sampling distribution Step 5: Determine the critical value, z, from the standard normal table Step 6: Develop the confidence interval estimate 10-38

39 The objective is to estimate the difference in mean time spent per visit for male and female customers of the fitness center. Previous studies indicate that the standard deviation is 11 minutes for males and 16 minutes for females. Develop a 95% confidence interval estimate for the difference in mean times. Step 1: Select independent samples from the two populations Step 2: Specify the desired confidence level Step 3: Compute the point estimate Step 4: Determine the standard error Step 5: Determine the critical value, z Step 6: Develop the confidence interval estimate 10-39

40 Assumptions: The populations are normally distributed The populations have equal variances The samples are independent Confidence interval estimate should be developed using the t-distribution 10-40

41 - Pooled standard deviation t - Critical t-value from the t-distribution, with degrees of freedom equal to n 1 + n

42 Step 1: Define the population parameter of interest and select independent samples from the two populations Step 2: Specify the confidence level Step 3: Compute the point estimate Step 4: Determine the standard error of sampling distribution Step 5: Determine the critical value, t, from the t-distribution table Step 6: Develop a confidence interval 10-42

43 t - Critical t-value from the t-distribution, with degrees of freedom equal to: 10-43

44 Step 1: Define the population parameter of interest and select independent samples from the two populations Step 2: Specify the desired confidence level Step 3: Compute the point estimate Step 4: Determine the standard error of the sampling distribution Step 5: Calculate the degrees of freedom and determine the critical value, t, from the t-distribution table Step 6: Develop the confidence interval estimate 10-44

45 10.2 Hypothesis Tests for Two Population Means Using Independent Samples Some situations require to test whether two populations have equal means or whether one population mean is larger (or smaller) then another These are hypothesis-testing applications Hypothesis Tests for Two Population Means The population standard deviations are known and the samples are independent The population standard deviations are unknown and the samples are independent 10-45

46 The Hypothesis-Testing Process for Two Population Means Step 1: Specify the population parameter of interest Step 2: Formulate the appropriate null and alternative hypotheses. The null hypothesis should contain the equality Variations in Hypothesis Testing 10-46

47 The Hypothesis-Testing Process for Two Population Means 10-47

48 The Hypothesis-Testing Process for Two Population Means - Example One-tailed (lower) Test Example: The company is interested in determining whether there is a difference in the average thickness of brick facing products made at the two plants. Plant 1 Plant

49 Using p-values 10-49

50 t-test Statistic: 10-50

51 The Hypothesis-Testing Process for Two Population Means - Example Two-tailed Test Example: Suppose an independent test agency wishes to conduct a test to determine whether name-brand ink cartridges generate more color pages on average than competing generic ink cartridges. Name-Brand Generic 10-51

52 The Hypothesis-Testing Process for Two Population Means - Example One-tailed (upper) Test Example: The leaders of the study are interested in determining whether there is a difference in mean annual contributions for individuals covered by TSAs and those with 401(k) retirement programs. TSA 401(k) 10-52

53 t-test Statistic: Degrees of Freedom: 10-53

54 10.3 Interval Estimation and Hypothesis Tests for Paired Samples Paired samples are dependent samples Samples that are selected in such a way that values in one sample are matched with the values in the second sample for the purpose of controlling for extraneous factors Examples Testing a new paint mix vs an old one Testing difference in gas mileage comparing regular and premium gas 10-54

55 Interval Estimation and Hypothesis Tests for Paired Samples x 1 and x 2 Values from samples 1 and 2, respectively d n d i i 1 n 10-55

56 Interval Estimation and Hypothesis Tests for Paired Samples s d n ( d i d ) i 1 n

57 Confidence Interval Estimate 10-57

58 Hypothesis Testing for Paired Samples t-test Statistic for Paired-Sample Test: 10-58

59 Hypothesis Testing for Paired Samples Variations in Hypothesis Testing Reject H 0 if t < -t /2 or t > t /2 Reject H 0 if t < -t Reject H 0 if t > t 10-59

60 Hypothesis Testing for Paired Samples - Example Suppose an independent test agency wishes to conduct a test to determine whether name-brand ink cartridges generate more color pages on average than competing generic ink cartridges. The test is conducted using paired samples. This means that the same people will use both types of cartridges, and the pages printed in each case will be recorded. Reject H 0 if t > t 10-60

61 Hypothesis Testing for Paired Samples - Solution User Name-Brand Generic d i The mean paired difference: The standard deviation for the paired differences: The t-test statistic: Decision and conclusion: Do not reject the null hypothesis 10-61

62 10.4 Estimation and Hypothesis Tests for Two Population Proportions 10-62

63 Estimation and Hypothesis Tests for Two Population Proportions Pooled Estimator for Overall Proportion: z-test Statistic for Difference between Population Proportions: 10-63

64 Hypothesis Testing for Two Population Proportions Variations in Hypothesis Testing 10-64

65 Hypothesis Testing for Two Population Proportions - Example A critical component of a handheld hair dryer is the motor-heater unit. Company has recently created a new motor-heater unit with fewer parts than the current unit. Company has decided to test samples of old and new units to see which motor-heater is more reliable. The null hypothesis states that the new motor-heater is no better than the old, or current, motor-heater. New Unit Old Unit 10-65

66 Analysis of Variance 12-1

67 Learning Outcomes Outcome 1. Understand the basic logic of analysis of variance. Outcome 2. Perform a hypothesis test for a single-factor design using analysis of variance manually and with the aid of Excel software. Outcome 3. Conduct and interpret post-analysis of variance pairwise comparison procedures. Outcome 4. Recognize when randomized block analysis of variance is useful and be able to perform analysis of variance on a randomized block design. Outcome 5. Perform analysis of variance on a two-factor design of experiments with replications using Excel and interpret the output

68 12.1 One-Way Analysis of Variance It is a common situation when someone needs to determine whether three or more populations have equal means ANOVA analysis of variance Completely Randomized Design: An experiment that consists of the independent random selection of observations representing each level of one factor 12-68

69 One-Way Analysis of Variance An analysis of variance design in which independent samples are obtained from two or more levels of a single factor for the purpose of testing whether the levels have equal means. Examples: Accident rates for 1 st, 2 nd, and 3 rd shift Expected mileage for five brands of tires 12-69

70 Introduction to One-Way ANOVA Factor: A quantity under examination in an experiment as a possible cause of variation in the response variable Levels: The categories, measurements, or strata of a factor of interest in the current experiment Balanced Design: An experiment has a balanced design if the factor levels have equal sample sizes

71 One-Way ANOVA Assumptions All populations are normally distributed. The population variances are equal. The observations are independent - that is, the occurrence of any one individual value does not affect the probability that any other observation will occur. The data are interval or ratio level

72 Hypotheses of One-Way ANOVA If the null hypothesis is true, the populations have identical distributions sample means for random samples from each population should be close in value The null hypothesis should be rejected only if the sample means are substantially different (some pairs may be the same) 12-72

73 Hypotheses of One-Way ANOVA 12-73

74 Partitioning the Sum of Squares Total Variation (SST): The aggregate dispersion of the individual data values across the various factor levels Within-Sample Variation (SSW): The dispersion that exists among the data values within a particular factor level Between Sample Variation (SSB): Dispersion among the factor sample means 12-74

75 Partitioned Sum of Squares SST - Total sum of squares SSB - Sum of squares between SSW - Sum of squares within 12-75

76 Total Sum of Squares i k n j i

77 Sum of Squares Between k i 1 Variation Due to Differences Among Groups 12-77

78 Sum of Squares Within i k n j i 1 1 Variation Due to Differences Within Groups 12-78

79 Mean Squares Mean Square Between Samples: Mean Square Within Samples: 12-79

80 One-Way ANOVA Table Source of Variation Between Samples Within Samples Total SS df MS F-Ratio SSB MSB SSW MSW SST 12-80

81 One-Way ANOVA - Example Company runs business in several locations. The VP of sales for the company is interested in knowing whether the dollar value for orders made by individual customers differs, on average, between the four locations. Business Locations Mean Variance n

82 One-Way ANOVA - Example Source of Variation SS df MS F-Ratio Between Samples Within Samples Total Draw a conclusion: 12-82

83 One-Way Analysis of Variance 12-83

84 One-Way Analysis of Variance Step 5: Determine the decision rule Step 6: Compute the total sum of squares, sum of squares between, and sum of squares within, and complete the ANOVA table. Step 7: Reach a decision Step 8: Draw a conclusion 12-84

85 Goodness-of-Fit Tests and Contingency Analysis 13-1

86 Learning Outcomes Outcome 1. Utilize the chi-square goodness-of-fit tests to determine whether data from a process fit a specified distribution. Outcome 2. Set up a contingency analysis table and perform a chi-square test of independence

87 13.1 Introduction to Goodness-of-Fit Tests Many of the statistical procedures introduced in earlier chapters require that the sample data come from populations that are normally distributed A statistical technique known as a goodness-of-fit test can be used to find whether the actual data from the process fit the probability distribution being considered

88 Introduction to Goodness-of-Fit Tests Examples: Are technical support calls equal across all days of the week? (i.e., do calls follow a uniform distribution?) Do measurements from a production process follow a normal distribution? 13-88

89 Chi-Square Goodness-of-Fit Test Statistic k i

90 Chi-Square Goodness-of-Fit Test - Example The company runs the same number of taxis Monday through Friday, with reduced staffing on Saturday and Sunday. This is because the operations manager believes that demand for taxicabs is fairly level throughout the week and about 25% less on weekends. The manager has decided to study demand to see whether the assumed demand pattern still applies

91 Chi-Square Goodness-of-Fit Test - Example Data: Test Statistic: Conclusion: 13-91

92 Chi-Square Goodness-of-Fit Test Step 1: Formulate the appropriate null and alternative hypotheses Step 2: Specify the significance level Step 3: Determine the critical value Step 4: Collect the sample data and compute the chi-square test statistic Step 5: Reach a decision Step 6: Draw a conclusion 13-92

93 Normal Distribution Example Company makes wood moldings, doorframes, and window frames. First they rip lumber in a smaller strips. The manufacturer of the saw claims that the ripsaw cuts an average deviation of zero from target and that the differences from target will be normally distributed, with a standard deviation of 0.01 inch. Company has recently become concerned that the ripsaw may not be cutting to the manufacturer s specifications. A quality improvement team selected a random sample of 300 boards just as they came off the ripsaw

94 Normal Distribution Example Conclusion: In this case, because the null hypothesis specified both the mean and the standard deviation, the normal distribution probabilities were computed using these values. If the mean and/or the standard deviation had not been specified, the sample mean and standard deviation would be used in the probability computation. You would lose one additional degree of freedom for each parameter that was estimated from the sample data

95 Chi-Square Goodness-of-Fit Test Step 1: Formulate the appropriate null and alternative hypotheses Step 2: Specify the level of significance Step 3: Determine the critical value Step 4: Collect the sample data and compute the chi-square test statistic Step 5: Reach a decision Step 6: Draw a conclusion 13-95

96 13.2 Introduction to Contingency Analysis Situations involving multiple population proportions Categorical data Used to classify sample observations according to two or more characteristics Chi-Square is used to determine independence of the characteristics of interest Data summarized in a contingency table 13-96

97 Contingency Table A table used to classify sample observations according to two or more identifiable characteristics It is also called a cross-tabulation table Example: Source of Funding vs. Gender (two variables) Source of Funding Gender Private State Male Female

98 Chi-Square Contingency Test Statistic r c i 1 j

99 Chi-Square Contingency Test - Example Contingency Table: Source of Funding Gender Private State Male 57 Female 164 Test Statistic: Conclusion: 13-99

100 2 x 2 Contingency Analysis Step 1: Specify the null and alternative hypotheses Step 2: Determine the significance level Step 3: Determine the critical value Step 4: Collect the sample data and compute the chi-square test statistic Step 5: Reach a decision Step 6: Draw a conclusion

101 r x c Contingency Table - Example Company pays market wages, provides competitive benefits, and offers attractive options for employees. However, several supervisors have complained that employee absenteeism is becoming a problem. In response to these complaints, the human resources manager studied a random sample of 500 employees. One aim of this study was to determine whether there is a relationship between absenteeism and marital status. Absenteeism during the past year was broken down into three levels: 0 absences; 1 to 5 absences; over 5 absences. Marital status was divided into four categories: Single; Married; Divorced; Widowed

102 r x c Contingency Table - Example Contingency Table: Absentee Rate Marital Status Over 5 Row Totals Single Married Divorced Widowed Column Totals Test Statistic: Conclusion:

103 r x c Contingency Table - Example 1. Open file. 2. Compute expected cell frequencies using Excel formula. 3. Compute chisquare statistic using Excel formula

104 Chi-square Test Limitations The chi-square distribution is only an approximation for the true distribution for contingency analysis The approximation is quite good when all expected cell frequencies are at least 5.0 When expected cell frequencies drop below 5.0, the calculated chi-square value tends to be inflated and may inflate the true probability of a Type I error beyond the stated significance level

105 Chi-square Test Limitations There are two alternatives that can be used to overcome the small expected-cellfrequency problem: Increase the sample size Combine the categories of the row and/or column variables

106 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America

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

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

Module 5 Hypotheses Tests: Comparing Two Groups

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

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

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

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

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

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

One-Way Analysis of Variance (ANOVA) Example Problem

One-Way Analysis of Variance (ANOVA) Example Problem One-Way Analysis of Variance (ANOVA) Example Problem Introduction Analysis of Variance (ANOVA) is a hypothesis-testing technique used to test the equality of two or more population (or treatment) means

More information

Study Guide for the Final Exam

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

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

Module 9: Nonparametric Tests. The Applied Research Center

Module 9: Nonparametric Tests. The Applied Research Center Module 9: Nonparametric Tests The Applied Research Center Module 9 Overview } Nonparametric Tests } Parametric vs. Nonparametric Tests } Restrictions of Nonparametric Tests } One-Sample Chi-Square Test

More information

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

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

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

Comparing Multiple Proportions, Test of Independence and Goodness of Fit

Comparing Multiple Proportions, Test of Independence and Goodness of Fit Comparing Multiple Proportions, Test of Independence and Goodness of Fit Content Testing the Equality of Population Proportions for Three or More Populations Test of Independence Goodness of Fit Test 2

More information

EXCEL Analysis TookPak [Statistical Analysis] 1. First of all, check to make sure that the Analysis ToolPak is installed. Here is how you do it:

EXCEL Analysis TookPak [Statistical Analysis] 1. First of all, check to make sure that the Analysis ToolPak is installed. Here is how you do it: EXCEL Analysis TookPak [Statistical Analysis] 1 First of all, check to make sure that the Analysis ToolPak is installed. Here is how you do it: a. From the Tools menu, choose Add-Ins b. Make sure Analysis

More information

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

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

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

Solutions to Homework 10 Statistics 302 Professor Larget

Solutions to Homework 10 Statistics 302 Professor Larget s to Homework 10 Statistics 302 Professor Larget Textbook Exercises 7.14 Rock-Paper-Scissors (Graded for Accurateness) In Data 6.1 on page 367 we see a table, reproduced in the table below that shows the

More information

Inferential Statistics

Inferential Statistics Inferential Statistics Sampling and the normal distribution Z-scores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are

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

Descriptive Analysis

Descriptive Analysis Research Methods William G. Zikmund Basic Data Analysis: Descriptive Statistics Descriptive Analysis The transformation of raw data into a form that will make them easy to understand and interpret; rearranging,

More information

One-Way Analysis of Variance

One-Way Analysis of Variance One-Way Analysis of Variance Note: Much of the math here is tedious but straightforward. We ll skim over it in class but you should be sure to ask questions if you don t understand it. I. Overview A. We

More information

Examining Differences (Comparing Groups) using SPSS Inferential statistics (Part I) Dwayne Devonish

Examining Differences (Comparing Groups) using SPSS Inferential statistics (Part I) Dwayne Devonish Examining Differences (Comparing Groups) using SPSS Inferential statistics (Part I) Dwayne Devonish Statistics Statistics are quantitative methods of describing, analysing, and drawing inferences (conclusions)

More information

9-3.4 Likelihood ratio test. Neyman-Pearson lemma

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

More information

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

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

12: Analysis of Variance. Introduction

12: Analysis of Variance. Introduction 1: Analysis of Variance Introduction EDA Hypothesis Test Introduction In Chapter 8 and again in Chapter 11 we compared means from two independent groups. In this chapter we extend the procedure to consider

More information

Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing

Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing 1) Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures

More information

Descriptive Statistics

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

More information

CHAPTER 13. Experimental Design and Analysis of Variance

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

More information

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

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

More information

Chapter 8 Hypothesis Tests. Chapter Table of Contents

Chapter 8 Hypothesis Tests. Chapter Table of Contents Chapter 8 Hypothesis Tests Chapter Table of Contents Introduction...157 One-Sample t-test...158 Paired t-test...164 Two-Sample Test for Proportions...169 Two-Sample Test for Variances...172 Discussion

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

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

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics. Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing

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

Elementary Statistics Sample Exam #3

Elementary Statistics Sample Exam #3 Elementary Statistics Sample Exam #3 Instructions. No books or telephones. Only the supplied calculators are allowed. The exam is worth 100 points. 1. A chi square goodness of fit test is considered to

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

Recall this chart that showed how most of our course would be organized:

Recall this chart that showed how most of our course would be organized: Chapter 4 One-Way ANOVA Recall this chart that showed how most of our course would be organized: Explanatory Variable(s) Response Variable Methods Categorical Categorical Contingency Tables Categorical

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

8 6 X 2 Test for a Variance or Standard Deviation

8 6 X 2 Test for a Variance or Standard Deviation Section 8 6 x 2 Test for a Variance or Standard Deviation 437 This test uses the P-value method. Therefore, it is not necessary to enter a significance level. 1. Select MegaStat>Hypothesis Tests>Proportion

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

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

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

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

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

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

More information

Factor B: Curriculum New Math Control Curriculum (B (B 1 ) Overall Mean (marginal) Females (A 1 ) Factor A: Gender Males (A 2) X 21

Factor B: Curriculum New Math Control Curriculum (B (B 1 ) Overall Mean (marginal) Females (A 1 ) Factor A: Gender Males (A 2) X 21 1 Factorial ANOVA The ANOVA designs we have dealt with up to this point, known as simple ANOVA or oneway ANOVA, had only one independent grouping variable or factor. However, oftentimes a researcher has

More information

Inferences About Differences Between Means Edpsy 580

Inferences About Differences Between Means Edpsy 580 Inferences About Differences Between Means Edpsy 580 Carolyn J. Anderson Department of Educational Psychology University of Illinois at Urbana-Champaign Inferences About Differences Between Means Slide

More information

Chapter 5 Analysis of variance SPSS Analysis of variance

Chapter 5 Analysis of variance SPSS Analysis of variance Chapter 5 Analysis of variance SPSS Analysis of variance Data file used: gss.sav How to get there: Analyze Compare Means One-way ANOVA To test the null hypothesis that several population means are equal,

More information

A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

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

More information

Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm

Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm

More information

Technology Step-by-Step Using StatCrunch

Technology Step-by-Step Using StatCrunch Technology Step-by-Step Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate

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

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

PASS Sample Size Software

PASS Sample Size Software Chapter 250 Introduction The Chi-square test is often used to test whether sets of frequencies or proportions follow certain patterns. The two most common instances are tests of goodness of fit using multinomial

More information

IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA

IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA CALIFORNIA STATE UNIVERSITY, LOS ANGELES INFORMATION TECHNOLOGY SERVICES IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA Summer 2013, Version 2.0 Table of Contents Introduction...2 Downloading the

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. 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

More information

1.5 Oneway Analysis of Variance

1.5 Oneway Analysis of Variance Statistics: Rosie Cornish. 200. 1.5 Oneway Analysis of Variance 1 Introduction Oneway analysis of variance (ANOVA) is used to compare several means. This method is often used in scientific or medical experiments

More information

ANOVA Analysis of Variance

ANOVA Analysis of Variance ANOVA Analysis of Variance What is ANOVA and why do we use it? Can test hypotheses about mean differences between more than 2 samples. Can also make inferences about the effects of several different IVs,

More information

Association Between Variables

Association Between Variables Contents 11 Association Between Variables 767 11.1 Introduction............................ 767 11.1.1 Measure of Association................. 768 11.1.2 Chapter Summary.................... 769 11.2 Chi

More information

Outline of Topics. Statistical Methods I. Types of Data. Descriptive Statistics

Outline of Topics. Statistical Methods I. Types of Data. Descriptive Statistics Statistical Methods I Tamekia L. Jones, Ph.D. (tjones@cog.ufl.edu) Research Assistant Professor Children s Oncology Group Statistics & Data Center Department of Biostatistics Colleges of Medicine and Public

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

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

Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures

Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 35487-0348 Phone:

More information

Tests of Hypotheses Using Statistics

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

More information

Measuring the Power of a Test

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

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

Data Analysis Tools. Tools for Summarizing Data

Data Analysis Tools. Tools for Summarizing Data Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool

More information

Statistical Inference and t-tests

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

More information

Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition

Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition Online Learning Centre Technology Step-by-Step - Excel Microsoft Excel is a spreadsheet software application

More information

Chapter 7. One-way ANOVA

Chapter 7. One-way ANOVA Chapter 7 One-way ANOVA One-way ANOVA examines equality of population means for a quantitative outcome and a single categorical explanatory variable with any number of levels. The t-test of Chapter 6 looks

More information

Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1. 1. Introduction p. 2. 2. Statistical Methods Used p. 5. 3. 10 and under Males p.

Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1. 1. Introduction p. 2. 2. Statistical Methods Used p. 5. 3. 10 and under Males p. Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1 Table of Contents 1. Introduction p. 2 2. Statistical Methods Used p. 5 3. 10 and under Males p. 8 4. 11 and up Males p. 10 5. 10 and under

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

Basic Statistics Self Assessment Test

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

More information

Course Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics

Course Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGraw-Hill/Irwin, 2010, ISBN: 9780077384470 [This

More information

UNDERSTANDING THE TWO-WAY ANOVA

UNDERSTANDING THE TWO-WAY ANOVA UNDERSTANDING THE e have seen how the one-way ANOVA can be used to compare two or more sample means in studies involving a single independent variable. This can be extended to two independent variables

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

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

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

Mind on Statistics. Chapter 15

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,

More information

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

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

More information

Difference of Means and ANOVA Problems

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

More information

Chapter 11. Chapter 11 Overview. Chapter 11 Objectives 11/24/2015. Other Chi-Square Tests

Chapter 11. Chapter 11 Overview. Chapter 11 Objectives 11/24/2015. Other Chi-Square Tests 11/4/015 Chapter 11 Overview Chapter 11 Introduction 11-1 Test for Goodness of Fit 11- Tests Using Contingency Tables Other Chi-Square Tests McGraw-Hill, Bluman, 7th ed., Chapter 11 1 Bluman, Chapter 11

More information

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

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

More information

ANOVA ANOVA. Two-Way ANOVA. One-Way ANOVA. When to use ANOVA ANOVA. Analysis of Variance. Chapter 16. A procedure for comparing more than two groups

ANOVA ANOVA. Two-Way ANOVA. One-Way ANOVA. When to use ANOVA ANOVA. Analysis of Variance. Chapter 16. A procedure for comparing more than two groups ANOVA ANOVA Analysis of Variance Chapter 6 A procedure for comparing more than two groups independent variable: smoking status non-smoking one pack a day > two packs a day dependent variable: number of

More information

Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools

Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools Occam s razor.......................................................... 2 A look at data I.........................................................

More information

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

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

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

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

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

Chapter 12 Sample Size and Power Calculations. Chapter Table of Contents

Chapter 12 Sample Size and Power Calculations. Chapter Table of Contents Chapter 12 Sample Size and Power Calculations Chapter Table of Contents Introduction...253 Hypothesis Testing...255 Confidence Intervals...260 Equivalence Tests...264 One-Way ANOVA...269 Power Computation

More information

Factorial Analysis of Variance

Factorial Analysis of Variance Chapter 560 Factorial Analysis of Variance Introduction A common task in research is to compare the average response across levels of one or more factor variables. Examples of factor variables are income

More information

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

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

More information

Section 13, Part 1 ANOVA. Analysis Of Variance

Section 13, Part 1 ANOVA. Analysis Of Variance Section 13, Part 1 ANOVA Analysis Of Variance Course Overview So far in this course we ve covered: Descriptive statistics Summary statistics Tables and Graphs Probability Probability Rules Probability

More information

Develop hypothesis and then research to find out if it is true. Derived from theory or primary question/research questions

Develop hypothesis and then research to find out if it is true. Derived from theory or primary question/research questions Chapter 12 Hypothesis Testing Learning Objectives Examine the process of hypothesis testing Evaluate research and null hypothesis Determine one- or two-tailed tests Understand obtained values, significance,

More information

Chapter 11-12 1 Review

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

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

Chi-square test Fisher s Exact test

Chi-square test Fisher s Exact test Lesson 1 Chi-square test Fisher s Exact test McNemar s Test Lesson 1 Overview Lesson 11 covered two inference methods for categorical data from groups Confidence Intervals for the difference of two proportions

More information

SPSS Tests for Versions 9 to 13

SPSS Tests for Versions 9 to 13 SPSS Tests for Versions 9 to 13 Chapter 2 Descriptive Statistic (including median) Choose Analyze Descriptive statistics Frequencies... Click on variable(s) then press to move to into Variable(s): list

More information

AP STATISTICS 2009 SCORING GUIDELINES (Form B)

AP STATISTICS 2009 SCORING GUIDELINES (Form B) AP STATISTICS 2009 SCORING GUIDELINES (Form B) Question 5 Intent of Question The primary goals of this question were to assess students ability to (1) state the appropriate hypotheses, (2) identify and

More information