# DIRECTIONS. Exercises (SE) file posted on the Stats website, not the textbook itself. See How To Succeed With Stats Homework on Notebook page 7!

Save this PDF as:

Size: px
Start display at page:

Download "DIRECTIONS. Exercises (SE) file posted on the Stats website, not the textbook itself. See How To Succeed With Stats Homework on Notebook page 7!"

## Transcription

1 Stats for Strategy HOMEWORK 3 (Topics 4 and 5) (revised spring 2015) DIRECTIONS Data files are available from the main Stats website for many exercises. (Smaller data sets for other exercises can be typed directly into MINITAB.) Use your own paper to write out and label the Four Steps of Hypothesis Testing. Use 5% significance whenever the textbook doesn t specify the level. Text exercises marked with the icon are accessed from the Supplementary Exercises (SE) file posted on the Stats website, not the textbook itself. See How To Succeed With Stats Homework on Notebook page 7! This is a great way to s-q-u-e-e-z-e as much knowledge and understanding as possible from the Homework for great quiz and exam preparation! A. Opening Data Files in Virtual Desktop. Using MINITAB for Chi-Square Tests To open a data set from the Stats website you must trick Virtual Desktop into opening the file from the university computer on which MINITAB is actually running! Do this by going through using Virtual Desktop s web browser, just as if you had opened a browser from a workstation in the Discussion computer lab. 1. Log on to Virtual Desktop: 2. Open the data file Topic 4 Example 1 from the Stats website. Use the steps below from within Virtual Desktop: Web Browsers > Firefox > Navigate to course website (it may be easiest to google Blake Whitten ) > Go to MINITAB Data Sets link, click the file to open Did you successfully open the file? (continued next page) 1

2 3. Now let s use MINITAB to get the three-in-one (observed, expected, contributions) χ 2 table shown for Topic 4 Example 1 on about page 92 in the Notebook. Open the Notes to about page 92. Do you see the MINITAB table? Use these MINITAB steps on your open Topic 4 Example 1 data file: Stat > Tables > Chi-Square Test for Association > (Choose Summarized data in a two-way table) > (Select columns Women, Men) > OK Your table probably shows two numbers in each cell instead of three (it s missing the contributions) so let s request all three from MINITAB. Re-run MINITAB and add these steps: Statistics > (Check box Each cell s contribution to chi-square) Now your table and the Notebook s table should match! Note: The correct χ 2 statistic is Pearson Chi-Square = Simply ignore the line below. (We won t use Likelihood Ratio Chi-Square = ) 4. Answer the following questions: (a) Find MINITAB s exact χ 2 statistic. (b) Find MINITAB s P -value. (c) Complete the Decision in Step 3: Is H 0 rejected? Why or why not? 2

3 B. Chi-Square Tests (Chapter 9) Exercise 9.36 (p. 518) Ignore the book s directions for this exercise. Follow these directions instead: (a) Calculate the degrees of freedom for the data table. (b) Look up the critical value for the χ 2 test at 5% significance. (c) Perform the χ 2 test in Four Steps. Refer to Topic 4 Example 2 in the Notes to recall how to do this. (Calculate χ 2 by hand in Step 2.) (d) Enter the data table into a MINITAB worksheet and perform the χ 2 test in MINITAB. What are MINITAB s exact χ 2 value and P -value? (e) Redo Step 3 of the Four Steps, using the P -value instead of critical value for your decision. (f) Use the 2 Proportions procedure in MINITAB to find and interpret a 95% CI for percent of general interest ads vs. men s ads which are not sexual. (g) Does the comparison of proportions in (f) reinforce or support the conclusion from the χ 2 test? Explain why or why not. (h) Use the 2 Proportions procedure in MINITAB to find and interpret a 95% CI for percent of women s ads vs. men s ads which are sexual. (i) Does the comparison in (h) reinforce or support the conclusion from the χ 2 test? Explain why or why not. (j) Use the table of χ 2 contributions to explain why one of the above pairs of proportions reinforces the χ 2 test but the other does not. Exercise 9.44 (Calculate χ 2 by hand, and use Four Steps. Do not use MINITAB.) Exercise 9.45 (Calculate χ 2 by hand, and use Four Steps. Do not use MINITAB.) Supplementary Exercise 9.8 (SE file p. 107) Use MINITAB and Four Steps. Also add part (b): (b) Choose two proportions whose comparison reinforces or supports the conclusion from the χ 2 test. Answer questions (i) (iii) below: (i) Define the proportions. (ii) Find and interpret a 95% confidence interval. (iii) Explain how the CI supports the χ 2 test. 3

5 Exercise 7.85 (p. 437) Exercise 7.86 D. Additional Practice (1) The American Automobile Association (AAA) is a national organization which also has 50 state chapters. Members of the Iowa chapter of the AAA would like to compare prices of regular gasoline to prices of diesel fuel within the state of Iowa. In particular, suppose that the Iowa chapter would like to test the theory that diesel is more expensive on average than regular gasoline at Iowa service stations on Sept. 30, It s known that fuel prices tend to vary by location, due to factors such as number of competing service stations nearby and transportation costs from the nearest refinery or fuel depot. The AAA national organization has provided the Iowa chapter with a database of prices, shown in the table below. The database was developed as follows: Five zip codes were randomly selected from all zip codes in the state of Minnesota, and five zip codes were randomly selected from all zip codes in the state of Iowa. For each selected zip code, the price of diesel fuel on Sept. 30, 2015 was recorded from a service station within that zip code. Also, the price of regular gas on Sept. 30, 2015 was recorded from a service station within the same zip code. (The stations measured for these two prices in any particular zip code are not necessarily the same.) Price (dollars/gallon) Price (dollars/gallon) Zip Code City State for Regular Gas for Diesel Fuel Minerva Iowa Ankeny Iowa Bethel Minnesota Marshall Minnesota Galt Iowa Becida Minnesota Pike Minnesota Miller Iowa Greeley Iowa Norwood Minnesota Avg. = Avg. = Test the theory, using 5% significance. (a) Choose the correct P -value from the following choices: (A) (B) (C) (D) (b) Decide. (c) Interpret. 5

6 (2) DIRECTIONS: Don t make any calculations or use MINITAB! Instead refer only to the MINITAB output on this page and the next. Market researchers think that background music might influence the mood and purchasing behavior of customers. One study in a supermarket in Northern Ireland compared three choices for the supermarket s sound system: no music, French accordion music, and Italian string music. Under each music choice, the researchers recorded the numbers of bottles of French, Italian, and other wine sold in one week. The data from the study are shown below. Music Wine None French Italian French Italian Other (a) Compare the choice of Italian music to the choice of no music for impact upon the relative popularity of Italian wine among customers. With 95% confidence, does this comparison support or reinforce the conclusion from the χ 2 test? (Choose the single best answer.) (A) Yes (B) No (C) Impossible to determine, based on the available MINITAB output (b) Compare the choice of French music to the choice of no music for impact upon the relative popularity of French wine among customers. With 95% confidence, does this comparison support or reinforce the conclusion from the χ 2 test? (A) Yes (B) No (C) Impossible to determine, based on the available MINITAB output None French Italian All All Pearson Chi-Square = , DF = 4, P-Value = Likelihood Ratio Chi-Square = , DF = 4, P-Value =

7 Test and CI for Two Proportions Estimate for difference: % CI for difference: ( , ) Test for difference = 0 (vs not = 0): Z = 1.61 P-Value = Test and CI for Two Proportions Estimate for difference: % CI for difference: ( , ) Test for difference = 0 (vs not = 0): Z = 2.03 P-Value = Test and CI for Two Proportions Estimate for difference: % CI for difference: ( , ) Test for difference = 0 (vs not = 0): Z = 1.34 P-Value = Test and CI for Two Proportions Estimate for difference: % CI for difference: ( , ) Test for difference = 0 (vs not = 0): Z = 2.07 P-Value = (end of assignment) 7

### Stats for Strategy Fall 2012 First-Discussion Handout: Stats Using Calculators and MINITAB

Stats for Strategy Fall 2012 First-Discussion Handout: Stats Using Calculators and MINITAB DIRECTIONS: Welcome! Your TA will help you apply your Calculator and MINITAB to review Business Stats, and will

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

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

### MATH Chapter 23 April 15 and 17, 2013 page 1 of 8 CHAPTER 23: COMPARING TWO CATEGORICAL VARIABLES THE CHI-SQUARE TEST

MATH 1342. Chapter 23 April 15 and 17, 2013 page 1 of 8 CHAPTER 23: COMPARING TWO CATEGORICAL VARIABLES THE CHI-SQUARE TEST Relationships: Categorical Variables Chapter 21: compare proportions of successes

### Chi-square (χ 2 ) Tests

Math 442 - Mathematical Statistics II May 5, 2008 Common Uses of the χ 2 test. 1. Testing Goodness-of-fit. Chi-square (χ 2 ) Tests 2. Testing Equality of Several Proportions. 3. Homogeneity Test. 4. Testing

### (More Practice With Trend Forecasts)

Stats for Strategy HOMEWORK 11 (Topic 11 Part 2) (revised Jan. 2016) DIRECTIONS/SUGGESTIONS You may conveniently write answers to Problems A and B within these directions. Some exercises include special

### 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

### SPSS: Expected frequencies, chi-squared test. In-depth example: Age groups and radio choices. Dealing with small frequencies.

SPSS: Expected frequencies, chi-squared test. In-depth example: Age groups and radio choices. Dealing with small frequencies. Quick Example: Handedness and Careers Last time we tested whether one nominal

### 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

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

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

### 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

### Analysis of categorical data: Course quiz instructions for SPSS

Analysis of categorical data: Course quiz instructions for SPSS The dataset Please download the Online sales dataset from the Download pod in the Course quiz resources screen. The filename is smr_bus_acd_clo_quiz_online_250.xls.

### UNIVERSITY OF IOWA Tippie College of Business Department of Economics ECON 2800 Statistics for Strategy Problems Summer 2015. Course Information

UNIVERSITY OF IOWA Tippie College of Business Department of Economics ECON 2800 Statistics for Strategy Problems Summer 2015 Course Information Overview We apply sophisticated statistical tools to aid

### STAT303 Spring 2014 Exam #2 Form A

1 STAT303 Spring 2014 Exam #2 Form A March 6, 2014 1. Don t even open this until you are told to do so. 2. Remember to turn your phone off now. 3. Please turn your hats around backwards or take them off.

### MINITAB ASSISTANT WHITE PAPER

MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. One-Way

### 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

### 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

### ED632G: Research/Applied Educational Psychology

1 ED632G: Research/Applied Educational Psychology This tutorial is designed to help ED632G students have a better understanding on how to run a general pre-test vs. posttest or improvement over semesters

### 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

### 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.

### Chapter 6: t test for dependent samples

Chapter 6: t test for dependent samples ****This chapter corresponds to chapter 11 of your book ( t(ea) for Two (Again) ). What it is: The t test for dependent samples is used to determine whether the

### 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

### Multiple Regression Analysis in Minitab 1

Multiple Regression Analysis in Minitab 1 Suppose we are interested in how the exercise and body mass index affect the blood pressure. A random sample of 10 males 50 years of age is selected and their

### 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

### Binary Diagnostic Tests Two Independent Samples

Chapter 537 Binary Diagnostic Tests Two Independent Samples Introduction An important task in diagnostic medicine is to measure the accuracy of two diagnostic tests. This can be done by comparing summary

### 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,

### Stats Review Chapters 9-10

Stats Review Chapters 9-10 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test

### Chi Square for Contingency Tables

2 x 2 Case Chi Square for Contingency Tables A test for p 1 = p 2 We have learned a confidence interval for p 1 p 2, the difference in the population proportions. We want a hypothesis testing procedure

### Online 12 - Sections 9.1 and 9.2-Doug Ensley

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

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

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

### Introduction to Stata and Hypothesis testing.

Introduction to Stata and Hypothesis testing. The goals today are simple let s open Stata, understand basically how it works, understand what a dofile is, and then run some basic hypothesis tests for testing

### 11. Analysis of Case-control Studies Logistic Regression

Research methods II 113 11. Analysis of Case-control Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:

### 1. Comparing Two Means: Dependent Samples

1. Comparing Two Means: ependent Samples In the preceding lectures we've considered how to test a difference of two means for independent samples. Now we look at how to do the same thing with dependent

### 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

### Testing Hypotheses using SPSS

Is the mean hourly rate of male workers \$2.00? T-Test One-Sample Statistics Std. Error N Mean Std. Deviation Mean 2997 2.0522 6.6282.2 One-Sample Test Test Value = 2 95% Confidence Interval Mean of the

### Part 1 Running a Hypothesis Test in Rcmdr

Math 17, Section 2 Spring 2011 Lab 7 Name SOLUTIONS Goal: To gain experience with hypothesis tests for a proportion Part 1 Running a Hypothesis Test in Rcmdr The goal of this part of the lab is to become

### Chapter 16 Appendix. Nonparametric Tests with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI-83-/84 Calculators

The Wilcoxon Rank Sum Test Chapter 16 Appendix Nonparametric Tests with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI-83-/84 Calculators These nonparametric tests make no assumption about Normality.

### Bivariate Analysis. Comparisons of proportions: Chi Square Test (X 2 test) Variable 1. Variable 2 2 LEVELS >2 LEVELS CONTINUOUS

Bivariate Analysis Variable 1 2 LEVELS >2 LEVELS CONTINUOUS Variable 2 2 LEVELS X 2 chi square test >2 LEVELS X 2 chi square test CONTINUOUS t-test X 2 chi square test X 2 chi square test ANOVA (F-test)

### 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

### Analysis of Variance. MINITAB User s Guide 2 3-1

3 Analysis of Variance Analysis of Variance Overview, 3-2 One-Way Analysis of Variance, 3-5 Two-Way Analysis of Variance, 3-11 Analysis of Means, 3-13 Overview of Balanced ANOVA and GLM, 3-18 Balanced

### Elements of Hypothesis Testing (Summary from lecture notes)

Statistics-20090 MINITAB - Lab 1 Large Sample Tests of Hypothesis About a Population Mean We use hypothesis tests to make an inference about some population parameter of interest, for example the mean

### 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. Steps for a hypothesis test:

Hypothesis Testing Steps for a hypothesis test: 1. State the claim H 0 and the alternative, H a 2. Choose a significance level or use the given one. 3. Draw the sampling distribution based on the assumption

### 1/22/2016. What are paired data? Tests of Differences: two related samples. What are paired data? Paired Example. Paired Data.

Tests of Differences: two related samples What are paired data? Frequently data from ecological work take the form of paired (matched, related) samples Before and after samples at a specific site (or individual)

### How To Run Statistical Tests in Excel

How To Run Statistical Tests in Excel Microsoft Excel is your best tool for storing and manipulating data, calculating basic descriptive statistics such as means and standard deviations, and conducting

### Lecture 28: Chapter 11, Section 1 Categorical & Quantitative Variable Inference in Paired Design

Lecture 28: Chapter 11, Section 1 Categorical & Quantitative Variable Inference in Paired Design Inference for Relationships: 2 Approaches CatQuan Relationship: 3 Designs Inference for Paired Design Paired

### One-Sample t-test. Example 1: Mortgage Process Time. Problem. Data set. Data collection. Tools

One-Sample t-test Example 1: Mortgage Process Time Problem A faster loan processing time produces higher productivity and greater customer satisfaction. A financial services institution wants to establish

Table of Contents Introduction to Minitab...2 Example 1 One-Way ANOVA...3 Determining Sample Size in One-way ANOVA...8 Example 2 Two-factor Factorial Design...9 Example 3: Randomized Complete Block Design...14

### 1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ

STA 3024 Practice Problems Exam 2 NOTE: These are just Practice Problems. This is NOT meant to look just like the test, and it is NOT the only thing that you should study. Make sure you know all the material

### AMS 5 HYPOTHESIS TESTING

AMS 5 HYPOTHESIS TESTING Hypothesis Testing Was it due to chance, or something else? Decide between two hypotheses that are mutually exclusive on the basis of evidence from observations. Test of Significance

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

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

### Mind on Statistics. Chapter 12

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

### 13.2 The Chi Square Test for Homogeneity of Populations The setting: Used to compare distribution of proportions in two or more populations.

13.2 The Chi Square Test for Homogeneity of Populations The setting: Used to compare distribution of proportions in two or more populations. Data is organized in a two way table Explanatory variable (Treatments)

### STAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico. Fall 2013

STAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico Fall 2013 CHAPTER 18 INFERENCE ABOUT A POPULATION MEAN. Conditions for Inference about mean

### 7.1 Inference for comparing means of two populations

Objectives 7.1 Inference for comparing means of two populations Matched pair t confidence interval Matched pair t hypothesis test http://onlinestatbook.com/2/tests_of_means/correlated.html Overview of

### SAS Software to Fit the Generalized Linear Model

SAS Software to Fit the Generalized Linear Model Gordon Johnston, SAS Institute Inc., Cary, NC Abstract In recent years, the class of generalized linear models has gained popularity as a statistical modeling

### TRIM: Web Tool. Web Address The TRIM web tool can be accessed at:

TRIM: Web Tool Accessing TRIM Records through the Web The TRIM web tool is primarily aimed at providing access to records in the TRIM system. While it is possible to place records into TRIM or amend records

### Chapter 23 Inferences About Means

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

### Do the following using Mintab (1) Make a normal probability plot for each of the two curing times.

SMAM 314 Computer Assignment 4 1. An experiment was performed to determine the effect of curing time on the comprehensive strength of concrete blocks. Two independent random samples of 14 blocks were prepared

### An SPSS companion book. Basic Practice of Statistics

An SPSS companion book to Basic Practice of Statistics SPSS is owned by IBM. 6 th Edition. Basic Practice of Statistics 6 th Edition by David S. Moore, William I. Notz, Michael A. Flinger. Published by

### Data Backup Procedure for Mac Users (Mac OS 10.4)

Data Backup Procedure for Mac Users (Mac OS 10.4) Teachers and Staff: It is important that you backup your documents before you leave for the summer. YOU are responsible for backing up your files. Please

### A) 0.1554 B) 0.0557 C) 0.0750 D) 0.0777

Math 210 - Exam 4 - Sample Exam 1) What is the p-value for testing H1: µ < 90 if the test statistic is t=-1.592 and n=8? A) 0.1554 B) 0.0557 C) 0.0750 D) 0.0777 2) The owner of a football team claims that

### General Method: Difference of Means. 3. Calculate df: either Welch-Satterthwaite formula or simpler df = min(n 1, n 2 ) 1.

General Method: Difference of Means 1. Calculate x 1, x 2, SE 1, SE 2. 2. Combined SE = SE1 2 + SE2 2. ASSUMES INDEPENDENT SAMPLES. 3. Calculate df: either Welch-Satterthwaite formula or simpler df = min(n

### Allelopathic Effects on Root and Shoot Growth: One-Way Analysis of Variance (ANOVA) in SPSS. Dan Flynn

Allelopathic Effects on Root and Shoot Growth: One-Way Analysis of Variance (ANOVA) in SPSS Dan Flynn Just as t-tests are useful for asking whether the means of two groups are different, analysis of variance

### LAB 4 ASSIGNMENT CONFIDENCE INTERVALS AND HYPOTHESIS TESTING. Using Data to Make Decisions

LAB 4 ASSIGNMENT CONFIDENCE INTERVALS AND HYPOTHESIS TESTING This lab assignment will give you the opportunity to explore the concept of a confidence interval and hypothesis testing in the context of a

### 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

### Name: Date: Use the following to answer questions 3-4:

Name: Date: 1. Determine whether each of the following statements is true or false. A) The margin of error for a 95% confidence interval for the mean increases as the sample size increases. B) The margin

### We know from STAT.1030 that the relevant test statistic for equality of proportions is:

2. Chi 2 -tests for equality of proportions Introduction: Two Samples Consider comparing the sample proportions p 1 and p 2 in independent random samples of size n 1 and n 2 out of two populations which

### Computer Lab 3 Thursday, 24 February, 2011 DMS 106 4:00 5:15PM

Statistics: Continuous Methods STAT452/652, Spring 2011 Computer Lab 3 Thursday, 24 February, 2011 DMS 106 4:00 5:15PM Goodness of Fit tests: Chi-square, Kolmogorov-Smirnov, Anderson-Darling, Shapiro-Wilk

### 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

### E205 Final: Version B

Name: Class: Date: E205 Final: Version B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of a local nightclub has recently surveyed a random

### CHI-Squared Test of Independence

CHI-Squared Test of Independence Minhaz Fahim Zibran Department of Computer Science University of Calgary, Alberta, Canada. Email: mfzibran@ucalgary.ca Abstract Chi-square (X 2 ) test is a nonparametric

### HOW TO USE MINITAB: INTRODUCTION AND BASICS. Noelle M. Richard 08/27/14

HOW TO USE MINITAB: INTRODUCTION AND BASICS 1 Noelle M. Richard 08/27/14 CONTENTS * Click on the links to jump to that page in the presentation. * 1. Minitab Environment 2. Uploading Data to Minitab/Saving

### Test of proportion = 0.5 N Sample prop 95% CI z- value p- value (0.400, 0.466)

STATISTICS FOR THE SOCIAL AND BEHAVIORAL SCIENCES Recitation #10 Answer Key PROBABILITY, HYPOTHESIS TESTING, CONFIDENCE INTERVALS Hypothesis tests 2 When a recent GSS asked, would you be willing to pay

### Lecture 7: Binomial Test, Chisquare

Lecture 7: Binomial Test, Chisquare Test, and ANOVA May, 01 GENOME 560, Spring 01 Goals ANOVA Binomial test Chi square test Fisher s exact test Su In Lee, CSE & GS suinlee@uw.edu 1 Whirlwind Tour of One/Two

### Using Minitab for Regression Analysis: An extended example

Using Minitab for Regression Analysis: An extended example The following example uses data from another text on fertilizer application and crop yield, and is intended to show how Minitab can be used to

### 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

### Paired 2 Sample t-test

Variations of the t-test: Paired 2 Sample 1 Paired 2 Sample t-test Suppose we are interested in the effect of different sampling strategies on the quality of data we recover from archaeological field surveys.

### 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

### Chapter 23. Two Categorical Variables: The Chi-Square Test

Chapter 23. Two Categorical Variables: The Chi-Square Test 1 Chapter 23. Two Categorical Variables: The Chi-Square Test Two-Way Tables Note. We quickly review two-way tables with an example. Example. Exercise

### 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

### 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

### 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

### Hypothesis testing: Examples. AMS7, Spring 2012

Hypothesis testing: Examples AMS7, Spring 2012 Example 1: Testing a Claim about a Proportion Sect. 7.3, # 2: Survey of Drinking: In a Gallup survey, 1087 randomly selected adults were asked whether they

### 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

### 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

### Analyzing tables. Chi-squared, exact and monte carlo tests. Jon Michael Gran Department of Biostatistics, UiO

Analyzing tables Chi-squared, exact and monte carlo tests Jon Michael Gran Department of Biostatistics, UiO MF9130 Introductory course in statistics Thursday 26.05.2011 1 / 50 Overview Aalen chapter 6.5,

### Solutions 7. Review, one sample t-test, independent two-sample t-test, binomial distribution, standard errors and one-sample proportions.

Solutions 7 Review, one sample t-test, independent two-sample t-test, binomial distribution, standard errors and one-sample proportions. (1) Here we debunk a popular misconception about confidence intervals

### Example for testing one population mean:

Today: Sections 13.1 to 13.3 ANNOUNCEMENTS: We will finish hypothesis testing for the 5 situations today. See pages 586-587 (end of Chapter 13) for a summary table. Quiz for week 8 starts Wed, ends Monday

### 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

### 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

### BIOM611 Biological Data Analysis

BIOM611 Biological Data Analysis Spring, 2015 Tentative Syllabus Introduction BIOMED611 is a ½ unit course required for all 1 st year BGS students (except GCB students). It will provide an introduction

### Statistics II Final Exam - January Use the University stationery to give your answers to the following questions.

Statistics II Final Exam - January 2012 Use the University stationery to give your answers to the following questions. Do not forget to write down your name and class group in each page. Indicate clearly

### AP Statistics 2004 Scoring Guidelines

AP Statistics 2004 Scoring Guidelines The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use must be sought

### Using CrunchIt (http://bcs.whfreeman.com/crunchit/bps4e) or StatCrunch (www.calvin.edu/go/statcrunch)

Using CrunchIt (http://bcs.whfreeman.com/crunchit/bps4e) or StatCrunch (www.calvin.edu/go/statcrunch) 1. In general, this package is far easier to use than many statistical packages. Every so often, however,

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

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

### STA 2023H Solutions for Practice Test 4

1. Which statement is not true about confidence intervals? A. A confidence interval is an interval of values computed from sample data that is likely to include the true population value. B. An approximate

### Hypothesis Testing hypothesis testing approach formulation of the test statistic

Hypothesis Testing For the next few lectures, we re going to look at various test statistics that are formulated to allow us to test hypotheses in a variety of contexts: In all cases, the hypothesis testing