# 1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

Size: px
Start display at page:

Download "1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96"

Transcription

1 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 of operation. To test the validity of this claim, a government testing agency selected a random sample of 100 sets and found that 14 sets required some repair within the first two years of operation. 1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = What is the standard error of this confidence interval? ˆp(1 ˆp).14(1.14) SE = = = n What is the margin of error? ME = CV SE = = Set up a 95% confidence interval estimate of the population proportion of TV sets that need repair in the first two years of operation? ( , ) 5. What conclusion can we draw from this confidence interval? Since 0.1 is within the confidence interval, we can conclude that the company s brochure is correct. 6. Interpret the 95% confidence interval. We are 95% confident that the true population proportion is between 8 and 21 percent. 7. What sample size should be taken if the agency wants 95% confidence when the margin of error is 0.05? n = ( CV ME )2 (ˆp(1 ˆp)) = ( )2 (.14(1.14) =

2 2.2 CI 2-independent samples Scenario 2 The purchasing director for an industrial factory is investigating the possibility of purchasing a new milling machine. She determines that the new machine will be purchased if there is evidence that the parts produced a higher breaking strength than those from the old machine. The sample standard deviation of the breaking strength for the old machine is 10 kilograms and for the new machine is 9 kilograms. A sample of 25 parts taken from the old machine indicated a sample mean of 65 kilograms, whereas a similar sample of 25 from the new machine indicated a sample mean of 72 kilograms. 1. What are the degrees of freedom? DF = n 1 + n 2 2 = = What is the critical value for this 95% confidence interval? CV = t 0.025,48 = invt (.025, 48) = ± What is the standard error of this confidence interval? Since ME = CV SE, we can solve for SE = ME = 5.41 = CV What is the margin of error? ME = = Set up a 95% confidence interval of the population difference between the two means? (-12.41, ) 6. What conclusion can we draw from this confidence interval? Since zero is not within the interval, we can conclude that the new machine has a higher breaking strength than the old machine. The purchasing director should purchase the new machine. 7. Interpret the 95% confidence interval. We are 95% confident that the true mean difference is between and

3 2.3 CI 1 sample T Scenario 3 Suppose an independent testing agency has been contracted to determine whether the contracting company should use a gasoline additive to increase gasoline mileage of its vehicles. The current gasoline mileage for it vehicles is 18.5 mpg. A random sample of 30 vehicles from the company s fleet produced a sample average of mpg and a sample standard deviation of 5.2 mpg. 1. What are the degrees of freedom? DF = n 1 = 30 1 = What is the critical value for this 95% confidence interval? CV = t.025,29 = invt (.025, 29) = ± What is the standard error of this confidence interval? SE = = What is the margin of error? ME = CV SE = = Set up a 95% confidence interval of the population average of the of MPG with gasoline additive? (17.398, ) 6. What conclusion can we draw from this confidence interval? The MPG does not significantly change when the additive was placed in the gasoline. 7. Interpret the 95% confidence interval. We are 95% confident that the true mean is between 17.4 and What sample size should be taken if the agency wants 95% confidence when the margin of error is 1.5? CV SD n = ( ME )2 = ( ) 2 =

4 2.4 CI paired t Scenario 4 Suppose a shoe company wants to test material for the soles of shoes. For each pair of shoes the new material is placed on one shoe and the old material is placed on the other shoe. After a given period of time a random sample of 10 pairs of shoes is selected. The wear is measured on a 10 point scale (higher is better) with the following results. The average of the differences is 0.3 and it standard deviation is What are the degrees of freedom? DF = n 1 = 10 1 = 9 2. What is the critical value for this 95% confidence interval? CV = t.025,9 = invt (.025, 9) = ± What is the standard error of this confidence interval? SE = SD n = = What is the margin of error? ME = CV SE = = Set up a 95% confidence interval of the population difference of paired observations of shoe soles? (-0.964, 1.564) 6. What conclusion can we draw from this confidence interval? Since zero is within the confidence interval, we can conclude that there is no difference between the new material and the old material. 7. Interpret the 95% confidence interval. We are 95% confident that the true average difference is between -0.9 and What sample size should be taken if the agency wants 95% confidence when the margin of error is 0.6? CV SD n = ( ME )2 = ( ) 2 =

5 2.5 hypotheses test 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 of operation. To test the validity of this claim, a government testing agency selected a random sample of 100 sets and found that 14 sets required some repair within the first two years of operation. The company uses a 5% level of significance. 1. How many tails have for this test? one-tailed which is upper-tail 2. What are the hypotheses? H 0 : p 0.1 vs. H 1 : p > What is the standard error of the proportion? p(1 p).1(1.1) SE = = = 0.03 n What is the test statistic? z = What is the p-value? p-value = ; do not reject H 0 6. What conclusion can we draw from this test? There is no evidence to reject the company s claim. 7. What is the critical value? z.05 = invnorm(.05) =

6 2.6 hypotheses test 2-independent samples Scenario 2 The purchasing director for an industrial factory is investigating the possibility of purchasing a new milling machine. She determines that the new machine will be purchased if there is evidence that the parts produced a higher breaking strength than those from the old machine. The sample standard deviation of the breaking strength for the old machine is 10 kilograms and for the new machine is 9 kilograms. A sample of 25 parts taken from the old machine indicated a sample mean of 65 kilograms, whereas a similar sample of 25 from the new machine indicated a sample mean of 72 kilograms. The director uses a 5% level of significance. 1. How many tails have for this test? one tailed test 2. What are the hypotheses? H 0 : µ o µ n vs. H 1 : µ o < µ n 3. What is the test statistic? t = What are the degrees of freedom? DF = n 1 + n 2 2 = = What is the p-value? p-value = Should you reject the null hypothesis (decision)? Yes 7. What conclusion can we draw from this test? There is evidence that the mean breaking strength of the new machine greater than the old machine. 8. What is the critical value? CV = t.05,48 = invt (.05, 48) =

7 2.7 Hypotheses testing 1 sample T Scenario 3 Suppose an independent testing agency has been contracted to determine whether the contracting company should use a gasoline additive. The current gasoline mileage for it vehicles is 18.5 mpg. A random sample of 30 vehicles from the company s fleet produced a sample average of mpg and a sample standard deviation of 5.2 mpg. Is there evidence that putting an additive into the gasoline of the company vehicles will improve the performance (i.e., MPG) of the company vehicles. The company uses a 5% level of significance. 1. How many tails have for this test? upper one-tailed test 2. What are the hypotheses? H 0 : µ 18.5 vs. H 1 : µ > What is the test statistic? t = What are the degrees of freedom? DF = n 1 = 30 1 = What is the p-value? p-value = Should you reject the null hypothesis (decision)? Do not reject H 0 7. What conclusion can we draw from this test? There is no evidence that the additive actual improved gasoline mileage. 8. What is the critical value? CV = t.05,29 = invt (.95, 29) =

8 2.8 Hypotheses test paired t Scenario 4 Suppose a shoe company wants to test material for the soles of shoes. For each pair of shoes the new material is placed on one shoe and the old material is placed on the other shoe. After a given period of time a random sample of 10 pairs of shoes is selected. The wear is measured on a 10 point scale (higher is better) with the following results. The average of the differences is 0.3 and it standard deviation is Is there evidence the new sole material is different from the current sole material? 1. How many tails have for this test? This is a two-tailed test. 2. What are the hypotheses? H 0 : µ d = 0 vs. H 1 : µ d 0 3. What is the test statistic? t = What are the degrees of freedom? DF = n 1 = 10 1 = 9 5. What is the p-value? p-value = Should you reject the null hypothesis (decision)? Do not reject H 0 7. What conclusion can we draw from this test? There is no evidence that the new sole material is different from the current sole material. 8. What is the critical value? CV = t.025,9 = invt (.025, 9) = ±

9 2.9 χ 2 -test Scenario 5 Suppose the head of the HR division of a mid-sized company wants to determine if she should let Red Cross have a give blood day in the company cafeteria. She take a random sample of size 49. The follow contingency table is constructed. Blood Donor Status Yes No Total Men Women Total What are the hypotheses? H 0 : p y = p n vs. H 1 : p y p n 2. What is the test statistic? χ 2 = What are the degrees of freedom? DF = (#r 1)(#c 1) = (2 1)(2 1) = 1 4. What is the p-value? p-value = Should you reject the null hypothesis (decision)? Is p-value < α? No; do not reject H 0 6. What conclusion can we draw from this test? There is evidence that status and gender are independent. 7. What is the expected value for cell row 2 column 2? E 2,2 =

10 2.10 SLR Scenario 6 A statistician for an American automobile manufacturer would like to develop a statistical model for predicting delivery time (the days between initiating the order to the actual delivery of the new car) of custom-ordered new automobile. The statistician believes there is a linear relationship between the number of options ordered on a car and the delivery time. A random sample of 16 cars is selected with the following results. Options Ordered vs Delivery Time Regression Statistics Multiple R R square Adj R sq Standard error Observations 16 Delivery Time Residuals Residuals vs Fitted Options Ordered Fitted values lm(time ~ Options) ANOVA df SS MS F Significance F Regression Residual Total Coefficients Coefficient Std error t Stat p-value Low 95% Up 95% intercept optionsordered Identify which variable is the X, independent, or explanatory variable. Options is the independent variable. 2. Identify which variable is the Y, dependent, or response variable. Time is the dependent variable. 3. Describe the pattern of points as they appear on the graph. As options increases, time increases. 4. What kind of relationship do you see? The relationship is positive and linear. 10

11 5. Are there any outliers? There are no apparent outliers. 6. Describe the strength and direction of the correlation. The strength of the correlation is strong (r =.98) and the direction is positive. 7. Compare this relationship with the pattern of points on the scatter diagram between the two variables. They are in agreement. 8. Write the specific estimated regression equation for this problem. time = b 0 + b 1 (options) = options 9. Using the estimated regression equation predict the average delivery time for the average car with 16 options ordered. time = = Is the previous prediction extrapolation? No, since the minimum options is 3 and the maximum options is Interpret the slope estimate, that is, explain what is means in terms of this problem. As options increases by one, time increases by 2.07 days (i.e., value of the slope). 12. Determine the coefficient of determination or how much variation in delivery time is accounted for by this regression model? Express your answer as a percent. What measure did you use to answer this question? Coefficient of determination = r 2 = 95.75%. 13. What is the standard error of the estimated regression line? Include the unit of measurement in your answer. s = days. 14. Using a 5% level of significance, is there evidence of a linear relationship between delivery time and options ordered? Be sure to state the hypotheses, test statistic, p-value, and the conclusion. H 0 : β = 0 vs. H 1 : β 0 t = p-value = 0 There is evidence that the slope is not zero. 11

12 15. Give a 95% confidence interval for the true (i.e., population) slope. (1.819, ) is a 95% confidence interval. 16. If the original correlation coefficient between these two variables were not known, how could it be calculated using the statistics in the regression output? How do you determine the sign of the correlation coefficient? r = r 2. The sign of r is determined by the sign of the slope. 17. Describe what you see on the residual plot. There appears to be a slight pattern. 18. For the data set, look at the 9 th pair of observations (Options, Time) or (12, 44). Calculate the residual, i.e., e i = Y i Ŷi. e 9 = 44 ( ) = = Is the model a good fit for the data? Be sure to state your decision and give the reasons that support your decision. Consider the following: r 2 =.9785 s = days Rejected H 0 of the slope. Review the scatter plot 12

13 2.11 MLR Scenario 7 Suppose a consumer organization wanted to develop a model to predict gasoline mileage as measured by miles per gallon (MPG) based on the horsepower of the car s engine and the weight of the car. A sample of 50 recent car models was selected, with the results summarized below. Regression Statistics Multiple R R square Adj R sq Standard error Observations 50 Correlation Coefficient MPG HP WT MPG 1 HP WT Descriptive Statistics MPG Horsepower Weight Mean Std Err Std Dev Variance Minimum Maximum Sum Count Min - Max x-variable Min Max HP WT ANOVA df SS MS F Significance F Regression Residual Total Coefficients Coefficient Std error t Stat p-value Low 95% Up 95% intercept Horsepower Weight Identify which variables are the X, independent, or explanatory variables. Horsepower (HP) and weight (WT) are the explanatory variables. 2. Identify which variable is the Y, dependent, or response variable. Miles per gallon (MPG) is the response variable. 13

14 3. Describe the strength and direction of the correlation. Correlation coefficient between MPG and HP is Correlation coefficient between MPG and WT is Correlation coefficient between WT and HP is Write the specific estimated regression equation for this problem. MP G = HP W T 5. Using the estimated regression equation predict the average MPG for a car that has 60 HP and weighs 2000 lbs. MP G = = 37.3mpg 6. Is the previous prediction extrapolation? No; since HP = 60 is between 48 and 165 and WT = 2000 is between 1755 and Interpret the slope estimate, that is, explain what is means in terms of this problem. Holding WT constant, as HP increasing be one, MPG decreases by Holding HP constant, as WT increasing be one, MPG decreases by Determine the coefficient of multiple determination or how much variation in MPG is accounted for by this regression model? Express your answer as a percent. What measure did you use to answer this question? r 2 = 74.9% 9. What is the standard error of the estimated regression line? Include the unit of measurement in your answer. s = mpg. 10. Using a 5% level of significance, is there evidence of a linear relationship between MPG and the explanatory variables? Be sure to state the hypotheses, test statistic, p-value, and the conclusion. H 0 : β 1 = β 2 = 0 vs. H 1 : at least one β i 0 where i = (1, 2) 11. Give a 95% confidence interval for the true (i.e., population) slope of MPG and HP. A 95% confidence interval for MPG and HP is (-.1832, ). 14

15 12. For the data set, look at the 1 st set of observations (MPG, HP, WT) or (43.1, 48, 1985). Calculate the residual, i.e., e i = Y i Ŷi. e 1 = 43.1 ( ) = = Is the model a good fit for the data? Be sure to state your decision and give the reasons that support your decision. r 2 =.7494 s = Rejected H 0 Questions Questions? 15

### 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

### 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

### 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

### Multiple Linear Regression

Multiple Linear Regression A regression with two or more explanatory variables is called a multiple regression. Rather than modeling the mean response as a straight line, as in simple regression, it is

### Univariate Regression

Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is

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

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

### 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

### 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,

### 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

### Outline. Topic 4 - Analysis of Variance Approach to Regression. Partitioning Sums of Squares. Total Sum of Squares. Partitioning sums of squares

Topic 4 - Analysis of Variance Approach to Regression Outline Partitioning sums of squares Degrees of freedom Expected mean squares General linear test - Fall 2013 R 2 and the coefficient of correlation

### Chapter 13 Introduction to Linear Regression and Correlation Analysis

Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing

### Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a

### 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

### 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

### Simple linear regression

Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between

### Week TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500 6 8480

1) The S & P/TSX Composite Index is based on common stock prices of a group of Canadian stocks. The weekly close level of the TSX for 6 weeks are shown: Week TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500

### Chapter 7: Simple linear regression Learning Objectives

Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) -

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

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

### Interaction between quantitative predictors

Interaction between quantitative predictors In a first-order model like the ones we have discussed, the association between E(y) and a predictor x j does not depend on the value of the other predictors

### 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 =

### Factors affecting online sales

Factors affecting online sales Table of contents Summary... 1 Research questions... 1 The dataset... 2 Descriptive statistics: The exploratory stage... 3 Confidence intervals... 4 Hypothesis tests... 4

### August 2012 EXAMINATIONS Solution Part I

August 01 EXAMINATIONS Solution Part I (1) In a random sample of 600 eligible voters, the probability that less than 38% will be in favour of this policy is closest to (B) () In a large random sample,

### Chapter 23. Inferences for Regression

Chapter 23. Inferences for Regression Topics covered in this chapter: Simple Linear Regression Simple Linear Regression Example 23.1: Crying and IQ The Problem: Infants who cry easily may be more easily

### Part 2: Analysis of Relationship Between Two Variables

Part 2: Analysis of Relationship Between Two Variables Linear Regression Linear correlation Significance Tests Multiple regression Linear Regression Y = a X + b Dependent Variable Independent Variable

### Simple Linear Regression Inference

Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation

### We extended the additive model in two variables to the interaction model by adding a third term to the equation.

Quadratic Models We extended the additive model in two variables to the interaction model by adding a third term to the equation. Similarly, we can extend the linear model in one variable to the quadratic

### 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

### 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.

### Regression step-by-step using Microsoft Excel

Step 1: Regression step-by-step using Microsoft Excel Notes prepared by Pamela Peterson Drake, James Madison University Type the data into the spreadsheet The example used throughout this How to is a regression

### " Y. Notation and Equations for Regression Lecture 11/4. Notation:

Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through

### Chapter 4 and 5 solutions

Chapter 4 and 5 solutions 4.4. Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in five gallon milk containers. The analysis is done in a laboratory,

### DATA INTERPRETATION AND STATISTICS

PholC60 September 001 DATA INTERPRETATION AND STATISTICS Books A easy and systematic introductory text is Essentials of Medical Statistics by Betty Kirkwood, published by Blackwell at about 14. DESCRIPTIVE

### 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

### 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

### 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

### 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

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

The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 130) Spring Semester 011 Chapter 10- TWO-SAMPLE TESTS Practice

### CHAPTER 13 SIMPLE LINEAR REGRESSION. Opening Example. Simple Regression. Linear Regression

Opening Example CHAPTER 13 SIMPLE LINEAR REGREION SIMPLE LINEAR REGREION! Simple Regression! Linear Regression Simple Regression Definition A regression model is a mathematical equation that descries the

### DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9

DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9 Analysis of covariance and multiple regression So far in this course,

### 2. Simple Linear Regression

Research methods - II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according

### 2013 MBA Jump Start Program. Statistics Module Part 3

2013 MBA Jump Start Program Module 1: Statistics Thomas Gilbert Part 3 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 2 1 Making an Investment Decision A researcher in your firm just

### 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

### 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,

### Chapter 7 Section 1 Homework Set A

Chapter 7 Section 1 Homework Set A 7.15 Finding the critical value t *. What critical value t * from Table D (use software, go to the web and type t distribution applet) should be used to calculate the

### Using Excel for inferential statistics

FACT SHEET Using Excel for inferential statistics Introduction When you collect data, you expect a certain amount of variation, just caused by chance. A wide variety of statistical tests can be applied

### Bill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1

Bill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1 Calculate counts, means, and standard deviations Produce

### 2. What is the general linear model to be used to model linear trend? (Write out the model) = + + + or

Simple and Multiple Regression Analysis Example: Explore the relationships among Month, Adv.\$ and Sales \$: 1. Prepare a scatter plot of these data. The scatter plots for Adv.\$ versus Sales, and Month versus

### Exercise 1.12 (Pg. 22-23)

Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.

### Point Biserial Correlation Tests

Chapter 807 Point Biserial Correlation Tests Introduction The point biserial correlation coefficient (ρ in this chapter) is the product-moment correlation calculated between a continuous random variable

### Example: Boats and Manatees

Figure 9-6 Example: Boats and Manatees Slide 1 Given the sample data in Table 9-1, find the value of the linear correlation coefficient r, then refer to Table A-6 to determine whether there is a significant

### MULTIPLE REGRESSION EXAMPLE

MULTIPLE REGRESSION EXAMPLE For a sample of n = 166 college students, the following variables were measured: Y = height X 1 = mother s height ( momheight ) X 2 = father s height ( dadheight ) X 3 = 1 if

### Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011

Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Name: Section: I pledge my honor that I have not violated the Honor Code Signature: This exam has 34 pages. You have 3 hours to complete this

### HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

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

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

### SIMPLE LINEAR CORRELATION. r can range from -1 to 1, and is independent of units of measurement. Correlation can be done on two dependent variables.

SIMPLE LINEAR CORRELATION Simple linear correlation is a measure of the degree to which two variables vary together, or a measure of the intensity of the association between two variables. Correlation

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

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

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

### Hypothesis Testing --- One Mean

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

### 5. Linear Regression

5. Linear Regression Outline.................................................................... 2 Simple linear regression 3 Linear model............................................................. 4

### 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

### 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

### 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

### Confidence Intervals for the Difference Between Two Means

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

### The Dummy s Guide to Data Analysis Using SPSS

The Dummy s Guide to Data Analysis Using SPSS Mathematics 57 Scripps College Amy Gamble April, 2001 Amy Gamble 4/30/01 All Rights Rerserved TABLE OF CONTENTS PAGE Helpful Hints for All Tests...1 Tests

### Using R for Linear Regression

Using R for Linear Regression In the following handout words and symbols in bold are R functions and words and symbols in italics are entries supplied by the user; underlined words and symbols are optional

### 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

### 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

### The importance of graphing the data: Anscombe s regression examples

The importance of graphing the data: Anscombe s regression examples Bruce Weaver Northern Health Research Conference Nipissing University, North Bay May 30-31, 2008 B. Weaver, NHRC 2008 1 The Objective

### INTERPRETING THE ONE-WAY ANALYSIS OF VARIANCE (ANOVA)

INTERPRETING THE ONE-WAY ANALYSIS OF VARIANCE (ANOVA) As with other parametric statistics, we begin the one-way ANOVA with a test of the underlying assumptions. Our first assumption is the assumption of

### 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

### 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

### Causal Forecasting Models

CTL.SC1x -Supply Chain & Logistics Fundamentals Causal Forecasting Models MIT Center for Transportation & Logistics Causal Models Used when demand is correlated with some known and measurable environmental

### Module 5: Multiple Regression Analysis

Using Statistical Data Using to Make Statistical Decisions: Data Multiple to Make Regression Decisions Analysis Page 1 Module 5: Multiple Regression Analysis Tom Ilvento, University of Delaware, College

### Predictor Coef StDev T P Constant 970667056 616256122 1.58 0.154 X 0.00293 0.06163 0.05 0.963. S = 0.5597 R-Sq = 0.0% R-Sq(adj) = 0.

Statistical analysis using Microsoft Excel Microsoft Excel spreadsheets have become somewhat of a standard for data storage, at least for smaller data sets. This, along with the program often being packaged

### Basic Statistics and Data Analysis for Health Researchers from Foreign Countries

Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Volkert Siersma siersma@sund.ku.dk The Research Unit for General Practice in Copenhagen Dias 1 Content Quantifying association

### 1 Simple Linear Regression I Least Squares Estimation

Simple Linear Regression I Least Squares Estimation Textbook Sections: 8. 8.3 Previously, we have worked with a random variable x that comes from a population that is normally distributed with mean µ and

### How Does My TI-84 Do That

How Does My TI-84 Do That A guide to using the TI-84 for statistics Austin Peay State University Clarksville, Tennessee How Does My TI-84 Do That A guide to using the TI-84 for statistics Table of Contents

### Stat 412/512 CASE INFLUENCE STATISTICS. Charlotte Wickham. stat512.cwick.co.nz. Feb 2 2015

Stat 412/512 CASE INFLUENCE STATISTICS Feb 2 2015 Charlotte Wickham stat512.cwick.co.nz Regression in your field See website. You may complete this assignment in pairs. Find a journal article in your field

### 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

### 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

### MULTIPLE LINEAR REGRESSION ANALYSIS USING MICROSOFT EXCEL. by Michael L. Orlov Chemistry Department, Oregon State University (1996)

MULTIPLE LINEAR REGRESSION ANALYSIS USING MICROSOFT EXCEL by Michael L. Orlov Chemistry Department, Oregon State University (1996) INTRODUCTION In modern science, regression analysis is a necessary part

### November 08, 2010. 155S8.6_3 Testing a Claim About a Standard Deviation or Variance

Chapter 8 Hypothesis Testing 8 1 Review and Preview 8 2 Basics of Hypothesis Testing 8 3 Testing a Claim about a Proportion 8 4 Testing a Claim About a Mean: σ Known 8 5 Testing a Claim About a Mean: σ

### 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

### NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )

Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates

### 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

### Relationships Between Two Variables: Scatterplots and Correlation

Relationships Between Two Variables: Scatterplots and Correlation Example: Consider the population of cars manufactured in the U.S. What is the relationship (1) between engine size and horsepower? (2)

### 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

### 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

### 1.1. Simple Regression in Excel (Excel 2010).

.. Simple Regression in Excel (Excel 200). To get the Data Analysis tool, first click on File > Options > Add-Ins > Go > Select Data Analysis Toolpack & Toolpack VBA. Data Analysis is now available under

### 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:

### 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

### HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

### Correlation and Simple Linear Regression

Correlation and Simple Linear Regression We are often interested in studying the relationship among variables to determine whether they are associated with one another. When we think that changes in a

### Section 1: Simple Linear Regression

Section 1: Simple Linear Regression Carlos M. Carvalho The University of Texas McCombs School of Business http://faculty.mccombs.utexas.edu/carlos.carvalho/teaching/ 1 Regression: General Introduction

### SPSS Guide: Regression Analysis

SPSS Guide: Regression Analysis I put this together to give you a step-by-step guide for replicating what we did in the computer lab. It should help you run the tests we covered. The best way to get familiar