# 4) The goodness of fit test is always a one tail test with the rejection region in the upper tail. Answer: TRUE

Save this PDF as:

Size: px
Start display at page:

Download "4) The goodness of fit test is always a one tail test with the rejection region in the upper tail. Answer: TRUE"

## Transcription

1 Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 13 Goodness of Fit Tests and Contingency Analysis 1) A goodness of fit test can be used to determine whether a set of sample data comes from a specific hypothesized population distribution. 2) If the test statistic for a chi square goodness of fit test is larger than the critical value, the null hypothesis should be rejected. 3) The logic behind the chi square goodness of fit test is based on determining how far the actual observed frequencies are from the expected frequencies. 4) The goodness of fit test is always a one tail test with the rejection region in the upper tail. 5) When the expected cell frequencies are smaller than 5, the cells should be combined in a meaningful way such that the expected cell frequencies do exceed 5. 6) The reason that a decision maker might want to combine groups before performing a goodness of fit test is to avoid accepting the null hypothesis due to an inflated value of the test statistic. Answer: FALSE 7) In a goodness of fit test, when the null hypothesis is true, the expected value for the chi square test statistic is zero. 8) The Conrad Real Estate Company recently conducted a statistical test to determine whether the number of days that homes are on the market prior to selling is normally distributed with a mean equal to 50 days and a standard deviation equal to 10 days. The sample of 200 homes was divided into 8 groups to form a grouped data frequency distribution. The degrees of freedom for the test will be 7. 9) The Conrad Real Estate Company recently conducted a statistical test to determine whether the number of days that homes are on the market prior to selling is normally distributed with a mean equal to 50 days and a standard deviation equal to 10 days. The sample of 200 homes was divided into 8 groups to form a grouped data frequency distribution. If a chi square goodness of fit test is to be conducted using an alpha =.05, the critical value is ) A business with 5 copy machines keeps track of how many copy machines need service on a given day. It believes this is binomially distributed with a probability of p = 0.2 of each machine needing service on any given day. It has collected the following based on a random sample of 100 days. X or 5 Frequency Given this information, assuming that all expected values are sufficiently large to use the classes as shown above, the critical value for testing the hypothesis will be based on 5 degrees of freedom. Answer: FALSE 11)Given this information the expected number of days on which exactly 1 machine breaks down is ) Given this information, assuming that all expected values are sufficiently large to use the classes as shown above, the critical value based on a 0.05 level of significance is ) It is believed that the number of drivers who are ticketed for speeding on a particular stretch of highway is a Poisson distribution with a mean of 3.5 per hour. A random sample of 100 hours is selected with the following results: X Frequency Given this information, and without regard to whether there is a need to combine cells due to expected cell frequencies, the critical value for testing whether the distribution is Poisson with a mean of 3.5 per hour at an alpha level of.05 is x2 = Answer: FALSE 13 1

5 58) Unlike the case of goodness of fit testing, with contingency analysis there is no restriction on the minimum size for an expected cell frequency. Answer: FALSE 59) In a contingency analysis the expected values are based on the assumption that the two variables are independent of each other. 60) If a contingency analysis test is performed with a 4 6 design, and if alpha =.05, the critical value from the chi square distribution is ) If a contingency analysis test performed with a 4 6 design results in a test statistic value of 18.72, and if alpha =.05, the null hypothesis that the row and column variable are independent should be rejected. Answer: FALSE 62) If the null hypothesis is not rejected, you do not need to worry when the expected cell frequencies drop below ) The degrees of freedom for the chi square goodness of fit test are equal to, where k is the number of categories. A) k + 1 B) k 1 C) k + 2 D) k 2 64) Which of the following statements is true in the context of a chi square goodness of fit test? A) The degrees of freedom for determining the critical value will be the number of categories minus 1. B) The critical value will come from the standard normal table if the sample size exceeds 30. C) The null hypothesis will be rejected for a small value of the test statistic. D) A very large test statistic will result in the null not being rejected. 65) A walk in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days. Frequency Mon 25 Tue 22 Wed 19 Thu 18 Fri 16 Total 100 Based on this information how many degrees for freedom are involved in this goodness of fit test? A) 99 B) 100 C) 4 D) 5 66) Assuming that a goodness of fit test is to be conducted using a 0.10 level of significance, the critical value is: A) B) C) D) ) To conduct a goodness of fit test, what is the expected value for Friday? A) 20 B) 25 C) 16 D) ) What is the value of the test statistic needed to conduct a goodness of fit test? A) 8.75 B) C) 2.46 D) ) Based on these data, conduct a goodness of fit test using a 0.10 level of significance. Which conclusion is correct? A) Arrivals are not uniformly distributed over the weekday because (test statistic) > (critical value). B) Arrivals are uniformly distributed over the weekday because (test statistic) > (critical value). C) Arrivals are not uniformly distributed over the weekday because (test statistic) < (critical value). D) Arrives are uniformly distributed over the weekday because (test statistic) < (critical value). 70) In a chi square goodness of fit test, by combining cells we guard against having an inflated test statistic that could have caused us to: 13 5

6 A) incorrectly reject the H0. B) incorrectly accept the H0. C) incorrectly reject the H1. D) incorrectly accept the H1. 71) In a goodness of fit test about a population distribution, if one or more parameters are left unspecified in H0, they must be estimated from the sample data. This will reduce the degrees of freedom by for each estimated parameter. A) 1 B) 2 C) 3 D) None of the above 72) If a sample with n = 60 subjects distributed over 3 categories was selected, a chi square test for goodness of fit will be used. How many degrees of freedom will be used in determining the chi square test statistic? A) 1 B) 2 C) 16 D) 64 73) Consider a goodness of fit test with a computed value of chi square = and a critical value = , the appropriate conclusion would be to: A) reject H0. B) fail to reject H0. C) take a larger sample. D) take a smaller sample. 74) A researcher is using a chi square test to determine whether there are any preferences among 4 brands of orange juice. With alpha = 0.05 and n = 30, the critical region for the hypothesis test would have a boundary of: A) 7.81 B) 8.71 C) 8.17 D) ) A chi square test for goodness of fit is used to test whether or not there are any preferences among 3 brands of peas. If the study uses a sample of n = 60 subjects, then the expected frequency for each category would be: A) 20 B) 30 C) 60 D) 33 76) We are interested in determining whether the opinions of the individuals on gun control (as to Yes, No, and No Opinion) are uniformly distributed. A sample of 150 was taken and the following data were obtained. Do you support gun control Number of Responses Yes 40 No 60 No Opinion 50 The conclusion of the test with alpha = 0.05 is that the views of people on gun control are: A) uniformly distributed. B) not uniformly distributed. C) inconclusive. D) None of the above 77) To use contingency analysis for numerical data, which of the following is true? A) Contingency analysis cannot be used for numerical data. B) Numerical data must be broken up into specific categories. C) Contingency analysis can be used for numerical data only if both variables are numerical. D) Contingency analysis can be used for numerical data only if it is interval data. 78) What does the term observed cell frequencies refer to? A) The frequencies found in the population being examined B) The frequencies found in the sample being examined C) The frequencies computed from H0 D) The frequencies computed from H1 79) What does the term expected cell frequencies refer to? A) The frequencies found in the population being examined B) The frequencies found in the sample being examined C) The frequencies computed from H0 D) the frequencies computed from H1 80) We expect the actual frequencies in each cell to approximately match the corresponding expected cell frequencies when: A) H0 is false. B) H0 is true. C) H0 is falsely accepted. D) the variables are related to each other. 81) In a contingency analysis, the greater the difference between the actual and the expected frequencies, the more likely: 13 6

7 A) H0 should be rejected. B) H0 should be accepted. C) we cannot determine H0. D) the smaller the test statistic will be. 82) In a chi square contingency analysis, when expected cell frequencies drop below 5, the calculated chi square value tends to be inflated and may inflate the true probability of beyond the stated significance level. A) committing a Type I error B) committing a Type II error C) Both A and B D) All of the above 83) In performing chi square contingency analysis, to overcome a small expected cell frequency problem, we: A) combine the categories of the row and/or column variables. B) increase the sample size. C) Both A and B D) None of the above 84) How can the degrees of freedom be found in a contingency table with cross classified data? A) When df are equal to rows minus columns B) When df are equal to rows multiplied by columns C) When df are equal to rows minus 1 multiplied by columns minus 1 D) Total number of cell minus 1 85) A cell phone company wants to determine if the use of text messaging is independent of age. The following data has been collected from a random sample of customers. Regularly use text messaging Do not regularly use text messaging Under and over 6 83 Based on the data above what is the expected value for the ʺunder 21 and regularly use text messagingʺ cell? A) 82 B) 50 C) 120 D) 58 86) To conduct a contingency analysis, the number of degrees of freedom is: A) 6 B) 5 C) 3 D) 2 87) To conduct a contingency analysis using a 0.01 level of significance, the value of the critical value is: A) B) C) D) ) To conduct a contingency analysis, the value of the test statistic is: A) B) 88.3 C) D) ) For a chi square test involving a contingency table, suppose H0 is rejected. We conclude that the two variables are: A) curvilinear. B) linear. C) related. D) not related. 90) When testing for independence in a contingency table with 3 rows and 4 columns, there are degrees of freedom. A) 5 B) 6 C) 7 D) 12 91) In testing a hypothesis that two categorical variables are independent using the x2 test, the expected cell frequencies are based on assuming: A) the null hypothesis. B) the alternative hypothesis. C) the normal distribution. D) the variable are related. 92) A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non Hispanic) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below. Hispanic Non Hispanic Seat belts worn Seat belts not worn Referring to these data, which test would be used to properly analyze the data in this experiment? A) x2 test for independence in a two way contingency table B) x2 test for equal proportions in a one way table 13 7

8 C) ANOVA F test for interaction in a 2 2 factorial design D) x2 goodness of fit test 93) Referring to these data, the calculated test statistic is: A) approximately B) nearly C) about D) approximately ) Referring to these data, which of the following conclusions should be reached if the appropriate hypothesis is conducted using an alpha =.05 level? A) The mean value for Hispanics is the same as for Non Hispanics. B) There is no relationship between whether someone is Hispanic and whether they wear a seat belt. C) The use of seat belts and whether a person is Hispanic or not is statistically related. D) None of the above 95) Many companies use well known celebrities as spokespeople in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below. Male Celebrity Female Celebrity Identified product Could not identify Referring to these sample data, which test would be used to properly analyze the data in this experiment? A) x2 test for independence in a two way contingency table B) x2 test for equal proportions in a one way table C) ANOVA F test for main treatment effect D) x2 goodness of fit test 96) Referring to these sample data, if the appropriate hypothesis test is to be conducted using a.05 level of significance, which of the following is correct critical value? A) B) C) 1.96 D) ) Referring to these sample data, which of the following values is the correct value of the test statistic? A) Approximately 9.48 B) Nearly 23.0 C) About 3.84 D) Approximately ) Referring to these sample data, if the appropriate null hypothesis is tested using a significance level equal to.05, which of the following conclusions should be reached? A) There is a relationship between gender of the celebrity and product identification. B) There is no relationship between gender of the celebrity and product identification. C) The mean number of products identified for males is different than the mean number for females. D) Females have higher brand awareness than males. 99) The degrees of freedom for a contingency table with 11 rows and 10 columns is: A) 11 B) 10 C) 110 D) ) We want to test whether type of car owned (domestic or foreign) is independent of gender. A contingence table is obtained from a sample of 990 people as At alpha = 0.05 level, we conclude that: A) x2= 3.34 and type of car owned is independent of gender. B) x2 = 3.34 and type of car owned is dependent of gender. C) x2 = 3.84 and type of car owned is independent of gender. D) x2 = 3.84 and type of car owned is dependent of gender. 13 8

9 101) The billing department of a national cable service company is conducting a study of how customers pay their monthly cable bills. The cable company accepts payment in one of four ways: in person at a local office, by mail, by credit card, or by electronic funds transfer from a bank account. The cable company randomly sampled 400 customers to determine if there is a relationship between the customerʹs age and the payment method used. The following sample results were obtained: Based on the sample data, can the cable company conclude that there is a relationship between the age of the customer and the payment method used? Conduct the appropriate test at the alpha= 0.01 level of significance. A) Because x2 = > , do not reject the null hypothesis. Based on the sample data conclude that age and type of payment are independent. B) Because x2 = > , reject the null hypothesis. Based on the sample data conclude that age and type of payment are not independent C) Because x2 = > , do not reject the null hypothesis. Based on the sample data conclude that age and type of payment are independent. D) Because x2 = > , reject the null hypothesis. Based on the sample data conclude that age and type of payment are not independent. 104) Explain why, in performing a goodness of fit test, it is sometimes necessary to combine categories. Answer: Because of the way in which the chi square test statistic is computed by squaring the difference between the observed and expected frequencies, when the expected frequencies are small (less than 5), the calculated test statistic can become artificially large and therefore may lead to an increased chance of committing a Type I statistical error. That is, a true null hypothesis may be rejected at a higher rate than indicated by the selected significance level. By combining categories, the small expected frequencies are grouped to become larger than five and thus the issue of inflated Type I error probability dissolves. Note: An alternative to combining categories is to increase the sample size. Large sample sizes result in greater expected cell frequencies in all categories. 13 9

### 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

### 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

### Statistical tests for SPSS

Statistical tests for SPSS Paolo Coletti A.Y. 2010/11 Free University of Bolzano Bozen Premise This book is a very quick, rough and fast description of statistical tests and their usage. It is explicitly

### 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

### 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

### 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

### 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

### 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

### Bivariate Statistics Session 2: Measuring Associations Chi-Square Test

Bivariate Statistics Session 2: Measuring Associations Chi-Square Test Features Of The Chi-Square Statistic The chi-square test is non-parametric. That is, it makes no assumptions about the distribution

### 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

### 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

### 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

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

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

### 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,

### 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

### 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

### 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

### Chapter 8 Introduction to Hypothesis Testing

Chapter 8 Student Lecture Notes 8-1 Chapter 8 Introduction to Hypothesis Testing Fall 26 Fundamentals of Business Statistics 1 Chapter Goals After completing this chapter, you should be able to: Formulate

### Crosstabulation & Chi Square

Crosstabulation & Chi Square Robert S Michael Chi-square as an Index of Association After examining the distribution of each of the variables, the researcher s next task is to look for relationships among

### Research Variables. Measurement. Scales of Measurement. Chapter 4: Data & the Nature of Measurement

Chapter 4: Data & the Nature of Graziano, Raulin. Research Methods, a Process of Inquiry Presented by Dustin Adams Research Variables Variable Any characteristic that can take more than one form or value.

### 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

### Test Positive True Positive False Positive. Test Negative False Negative True Negative. Figure 5-1: 2 x 2 Contingency Table

ANALYSIS OF DISCRT VARIABLS / 5 CHAPTR FIV ANALYSIS OF DISCRT VARIABLS Discrete variables are those which can only assume certain fixed values. xamples include outcome variables with results such as live

### 11-2 Goodness of Fit Test

11-2 Goodness of Fit Test In This section we consider sample data consisting of observed frequency counts arranged in a single row or column (called a one-way frequency table). We will use a hypothesis

### 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

### 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

### Mind on Statistics. Chapter 4

Mind on Statistics Chapter 4 Sections 4.1 Questions 1 to 4: The table below shows the counts by gender and highest degree attained for 498 respondents in the General Social Survey. Highest Degree Gender

### 7 Hypothesis testing - one sample tests

7 Hypothesis testing - one sample tests 7.1 Introduction Definition 7.1 A hypothesis is a statement about a population parameter. Example A hypothesis might be that the mean age of students taking MAS113X

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

Chi-square Goodness of Fit Test The chi-square test is designed to test differences whether one frequency is different from another frequency. The chi-square test is designed for use with data on a nominal

### TABLE OF CONTENTS. About Chi Squares... 1. What is a CHI SQUARE?... 1. Chi Squares... 1. Hypothesis Testing with Chi Squares... 2

About Chi Squares TABLE OF CONTENTS About Chi Squares... 1 What is a CHI SQUARE?... 1 Chi Squares... 1 Goodness of fit test (One-way χ 2 )... 1 Test of Independence (Two-way χ 2 )... 2 Hypothesis Testing

### DEPARTMENT OF POLITICAL SCIENCE AND INTERNATIONAL RELATIONS. Posc/Uapp 816 CONTINGENCY TABLES

DEPARTMENT OF POLITICAL SCIENCE AND INTERNATIONAL RELATIONS Posc/Uapp 816 CONTINGENCY TABLES I. AGENDA: A. Cross-classifications 1. Two-by-two and R by C tables 2. Statistical independence 3. The interpretation

### How to Conduct a Hypothesis Test

How to Conduct a Hypothesis Test The idea of hypothesis testing is relatively straightforward. In various studies we observe certain events. We must ask, is the event due to chance alone, or is there some

### The Chi-Square Test. STAT E-50 Introduction to Statistics

STAT -50 Introduction to Statistics The Chi-Square Test The Chi-square test is a nonparametric test that is used to compare experimental results with theoretical models. That is, we will be comparing observed

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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.

### 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,

### CHAPTER 14 ORDINAL MEASURES OF CORRELATION: SPEARMAN'S RHO AND GAMMA

CHAPTER 14 ORDINAL MEASURES OF CORRELATION: SPEARMAN'S RHO AND GAMMA Chapter 13 introduced the concept of correlation statistics and explained the use of Pearson's Correlation Coefficient when working

### 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

### 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,

### Contingency Tables and the Chi Square Statistic. Interpreting Computer Printouts and Constructing Tables

Contingency Tables and the Chi Square Statistic Interpreting Computer Printouts and Constructing Tables Contingency Tables/Chi Square Statistics What are they? A contingency table is a table that shows

### Biostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY

Biostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY 1. Introduction Besides arriving at an appropriate expression of an average or consensus value for observations of a population, it is important to

### CHAPTER 11. GOODNESS OF FIT AND CONTINGENCY TABLES

CHAPTER 11. GOODNESS OF FIT AND CONTINGENCY TABLES The chi-square distribution was discussed in Chapter 4. We now turn to some applications of this distribution. As previously discussed, chi-square is

### Statistics 2014 Scoring Guidelines

AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home

### CONTINGENCY TABLES ARE NOT ALL THE SAME David C. Howell University of Vermont

CONTINGENCY TABLES ARE NOT ALL THE SAME David C. Howell University of Vermont To most people studying statistics a contingency table is a contingency table. We tend to forget, if we ever knew, that contingency

### 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

### 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

### Chi Square Goodness of Fit & Two-way Tables (Create) MATH NSPIRED

Overview In this activity, you will look at a setting that involves categorical data and determine which is the appropriate chi-square test to use. You will input data into a list or matrix and conduct

### Chapter 8. Hypothesis Testing

Chapter 8 Hypothesis Testing Hypothesis In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing

### 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

### 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

### First-year Statistics for Psychology Students Through Worked Examples

First-year Statistics for Psychology Students Through Worked Examples 1. THE CHI-SQUARE TEST A test of association between categorical variables by Charles McCreery, D.Phil Formerly Lecturer in Experimental

### 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

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

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

### MBA 611 STATISTICS AND QUANTITATIVE METHODS

MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 1-11) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain

### 2012 Traffic Safety Behaviors Survey Minnesota Department of Public Safety, Office of Traffic Safety

This document is made available electronically by the Minnesota Legislative Reference Library as part of an ongoing digital archiving project. http://www.leg.state.mn.us/lrl/lrl.asp 2012 Traffic Safety

### Elementary Statistics

lementary Statistics Chap10 Dr. Ghamsary Page 1 lementary Statistics M. Ghamsary, Ph.D. Chapter 10 Chi-square Test for Goodness of fit and Contingency tables lementary Statistics Chap10 Dr. Ghamsary Page

### 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

### 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

### 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

### 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

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

Name: Class: Date: HypoTesting Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A Type II error is committed if we make: a. a correct decision when the

### Recommend Continued CPS Monitoring. 63 (a) 17 (b) 10 (c) 90. 35 (d) 20 (e) 25 (f) 80. Totals/Marginal 98 37 35 170

Work Sheet 2: Calculating a Chi Square Table 1: Substance Abuse Level by ation Total/Marginal 63 (a) 17 (b) 10 (c) 90 35 (d) 20 (e) 25 (f) 80 Totals/Marginal 98 37 35 170 Step 1: Label Your Table. Label

### CHAPTER IV FINDINGS AND CONCURRENT DISCUSSIONS

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

### HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION

HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION HOD 2990 10 November 2010 Lecture Background This is a lightning speed summary of introductory statistical methods for senior undergraduate

### Lecture 42 Section 14.3. Tue, Apr 8, 2008

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

### Multiple Hypothesis Testing: The F-test

Multiple Hypothesis Testing: The F-test Matt Blackwell December 3, 2008 1 A bit of review When moving into the matrix version of linear regression, it is easy to lose sight of the big picture and get lost

### CHAPTER 11 CHI-SQUARE AND F DISTRIBUTIONS

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

### II. DISTRIBUTIONS distribution normal distribution. standard scores

Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,

### MATH 10: Elementary Statistics and Probability Chapter 9: Hypothesis Testing with One Sample

MATH 10: Elementary Statistics and Probability Chapter 9: Hypothesis Testing with One Sample Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of

### Topic 8. Chi Square Tests

BE540W Chi Square Tests Page 1 of 5 Topic 8 Chi Square Tests Topics 1. Introduction to Contingency Tables. Introduction to the Contingency Table Hypothesis Test of No Association.. 3. The Chi Square Test

### 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

### Variables and Data A variable contains data about anything we measure. For example; age or gender of the participants or their score on a test.

The Analysis of Research Data The design of any project will determine what sort of statistical tests you should perform on your data and how successful the data analysis will be. For example if you decide

### Statistics I for QBIC. Contents and Objectives. Chapters 1 7. Revised: August 2013

Statistics I for QBIC Text Book: Biostatistics, 10 th edition, by Daniel & Cross Contents and Objectives Chapters 1 7 Revised: August 2013 Chapter 1: Nature of Statistics (sections 1.1-1.6) Objectives

### 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

### 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 =

### Introduction to Quantitative Methods

Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................

### 2015 Arkansas Driver s Survey 42 questions July 7, 2015

2015 Arkansas Driver s Survey 42 questions July 7, 2015 Hello, my name is from the University of Arkansas at Little Rock. We are doing a short survey asking Arkansans about their driving practices. We

### Premaster Statistics Tutorial 4 Full solutions

Premaster Statistics Tutorial 4 Full solutions Regression analysis Q1 (based on Doane & Seward, 4/E, 12.7) a. Interpret the slope of the fitted regression = 125,000 + 150. b. What is the prediction for

### statistics Chi-square tests and nonparametric Summary sheet from last time: Hypothesis testing Summary sheet from last time: Confidence intervals

Summary sheet from last time: Confidence intervals Confidence intervals take on the usual form: parameter = statistic ± t crit SE(statistic) parameter SE a s e sqrt(1/n + m x 2 /ss xx ) b s e /sqrt(ss

### Section 12 Part 2. Chi-square test

Section 12 Part 2 Chi-square test McNemar s Test Section 12 Part 2 Overview Section 12, Part 1 covered two inference methods for categorical data from 2 groups Confidence Intervals for the difference of

### Chapter 13. Chi-Square. Crosstabs and Nonparametric Tests. Specifically, we demonstrate procedures for running two separate

1 Chapter 13 Chi-Square This section covers the steps for running and interpreting chi-square analyses using the SPSS Crosstabs and Nonparametric Tests. Specifically, we demonstrate procedures for running

### Testing differences in proportions

Testing differences in proportions Murray J Fisher RN, ITU Cert., DipAppSc, BHSc, MHPEd, PhD Senior Lecturer and Director Preregistration Programs Sydney Nursing School (MO2) University of Sydney NSW 2006

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

Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data. 1) Bill kept track of the number of hours he spent

### 4. CHI-SQUARE: INTRODUCING THE GOODNESS OF FIT TEST AND THE TEST OF ASSOCIATION

4. : INRODUCING HE GOODNESS OF FI ES AND HE ES OF ASSOCIAION Dr om Clark & Dr Liam Foster Department of Sociological Studies University of Sheffield CONENS 4. Chi-square *So now you should be able to undertake

### Main Effects and Interactions

Main Effects & Interactions page 1 Main Effects and Interactions So far, we ve talked about studies in which there is just one independent variable, such as violence of television program. You might randomly

### 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

### 3. Nonparametric methods

3. Nonparametric methods If the probability distributions of the statistical variables are unknown or are not as required (e.g. normality assumption violated), then we may still apply nonparametric tests

### CATEGORICAL DATA Chi-Square Tests for Univariate Data

CATEGORICAL DATA Chi-Square Tests For Univariate Data 1 CATEGORICAL DATA Chi-Square Tests for Univariate Data Recall that a categorical variable is one in which the possible values are categories or groupings.

### 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

### AP: LAB 8: THE CHI-SQUARE TEST. Probability, Random Chance, and Genetics

Ms. Foglia Date AP: LAB 8: THE CHI-SQUARE TEST Probability, Random Chance, and Genetics Why do we study random chance and probability at the beginning of a unit on genetics? Genetics is the study of inheritance,

2. DATA AND EXERCISES (Geos2911 students please read page 8) 2.1 Data set The data set available to you is an Excel spreadsheet file called cyclones.xls. The file consists of 3 sheets. Only the third is