# Final Exam Practice Problem Answers

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 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 Calories: The number of calories per serving Protein: The number of grams of protein per serving Fat: The number of grams of fat per serving Fiber: The number of grams of fiber per serving Sodium: The number of milligrams (mg) of sodium per serving Carbo: The number of grams of carbohydrates per serving Sugars: The number of grams of sugars per serving Vitamins: The percentage of the recommended daily allowance (RDA) of vitamins per serving Shelf: 1 indicates that the cereal appears on the lowest shelf in the store indicates that the cereal does not appear on the lowest shelf in the store rating: An overall healthiness rating for the cereal. The higher the rating, the healthier the cereal. Some observations from the data set follow: name calories protein fat sodium fiber carbo sugars vitamins Shelf rating Product_ Cheerios Corn_Flakes Rice_Krispies Corn_Chex The Excel output below gives information about the sodium content in the 77 cereals. Use this to answer the following questions sodium Mean Standard Error Median 18 Mode Standard Deviation Sample Variance Kurtosis Skewness Range 32 Minimum Maximum 32 Sum Count 77 Confidence Level(9.%) sodium Min Q1 13 Median 18 Q3 21 Max 32 Outliers 1

2 1. Describe the shape of the distribution of sodium contents in the 77 breakfast cereals. The distribution is slightly skewed to the left and contains 9 outliers. These outliers all appear as one point on the boxplot because each of the 9 outlying cereals contain mg of sodium per serving. 2. What is the median sodium content in the cereals? What does this value represent? The median sodium content in the cereals is 18 mg. This implies that 5% of the cereals in the sample have less than 18 mg. of sodium per serving. Likewise, 5% of the cereals in the sample have more than 18 mg. of sodium per serving. 3. The 25% of the cereals that contain the most sodium contain at least how much sodium per serving? This value would be 75 th percentile or the 3 rd quartile. The 25% of the cereals with most sodium contain at least 21 mg per serving. 4. What is the standard deviation of the sodium contents? What does this value represent? The standard deviation of the sodium contents is This is a measure of variability in the sample. Specifically it measures the spread of the observations around the sample mean. 5. Assume that this represents a random sample of 77 cereals from the population of all breakfast cereals. Conduct a hypothesis test to determine if the mean sodium content in all cereals is greater than 14 mg. per serving. State the null and alternative hypothesis, the test statistic, p- value or an approximate p-value, and the decision and conclusion. Use α =.1 Ho: µ = 14 Ha: µ > 14 x µ Test statistic: t = = = 2.6 s n 77 Degrees of freedom: n-1 = 76 p-value: use approximate degrees of freedom of 8 on the t-table. Note that the computed test statistic falls between the critical values of 1.99 and 2.88 on the t-table. This implies that the p-value falls in the range.2 < p-value <.25. Decision: Since the p-value is greater than α, we will not reject the null hypothesis. There is not sufficient evidence at the 1% level of significance to conclude that the mean sodium content in all cereals is greater than 14 mg per serving. 6. What is the IQR of the sample? What does this value represent? The IQR gives the range of the middle 5% of the sample. It is the difference between the third and first quartiles and is given by Q3-Q1 = = 8. The following Excel output gives information about the healthiness ratings of cereals that appear on the low shelf in the store compared to the ratings of cereals that do not appear on the low shelf in the store. The output was generated using α =.5. Use this output to answer the following questions. Assume that the data represent random samples from the populations of all cereals on the low shelf and those not on the low shelf in the store. 2

3 7. What is the sample variance of the healthiness rating of cereals that do not appear on the low shelf? s 2 = Suppose you wish to conduct a hypothesis test to determine if cereals on the low shelf have a lower average healthiness rating than those appearing on higher shelves. State the null and alternative hypothesis to test this claim. H : µ low = µ hi H a : µ low < µ hi 9. State the test statistic, p-value, decision, and conclusion to the hypothesis test in the previous question. Use α =.5 Test statistic: p-value:.2 Decision: Since the p-value is less than α, reject H. There is sufficient evidence to conclude that cereals on the low shelf have lower average healthiness ratings than those that do not appear on the low shelf. 1. Compute and interpret a 95% confidence interval to estimate the difference in the population mean healthiness ratings between cereals that appear on the lower shelf and those on higher shelves. 2 2 s1 s ( x 1 x2 ) ± t * + = ± n n = ± 2.32(3.51) = ± With 95% confidence, on average cereals on the low shelf in the grocery store have a rating of between 3.45 and points lower than cereals on higher shelves. 3

4 11. What is the margin of error for the confidence interval computed in the previous question? The margin of error for the interval computed above is Suppose that the 77 cereals represent a random sample of all breakfast cereals. 21 of the cereals contain more than 1 grams of sugar per serving. Use this information to answer the following questions. 12. Compute a 99% confidence interval to estimate the true proportion of breakfast cereals that contain more than 1 grams of sugar per serving. Interpret the interval. x p = = =.284 n (.155,.413) ( p ) ( ) * p p ± z =.284 ± n ( ) =.284 ± =.284 ±.1291 = We are 99% confident that the true population proportion of all breakfast cereals that contain more than 1 grams of sugar per serving is between 16% and 41%. 13. A consumer health advocacy group states that more than one quarter of all breakfast cereals contain more than 1 grams of sugar per serving. State the null and alternative hypothesis to test this claim. Ho: p =.25 Ha: p > For the test in the previous question, state the test statistic, p-value, decision and conclusion. Use α =.1 x 21 pˆ = = =.2727 n 77 Test statistic: pˆ p z = = p 1 p ( ) ( ) n =.4935 =.46 p-value:.3228 Decision: Since the p-value is greater than α, do not reject Ho. There is not enough evidence at the 1% level of significance to conclude that more than one quarter of all breakfast cereals contain more than 1 grams of sugar. 4

5 The following table gives a breakdown of the shelf on which the cereal appears (shelf = 1 indicates the low shelf, shelf = indicates a higher shelf), and the manufacturer of the cereal. Self = 1 Shelf = Row totals General Mills Kellogg Nabisco Quaker Other Column totals Use this table information to test for the independence between the two categorical variables, shelf and manufacturer. State the null and alternative hypothesis, compute the test statistic, and give an approximate p-value for the test. State your decision and conclusion based on α =.5. Ho: The shelf on which a cereal appears is independent of the manufacturer. Ha: The shelf on which a cereal appears depends on the manufacturer. Table of expected cell counts: Table of ( actual expected )2 expected Self = 1 Shelf = Row totals General Mills Kellogg Nabisco Quaker Other Column totals Self = 1 General Mills Kellogg Nabisco Quaker Other Shelf = Row totals Column totals Test statistic: Degrees of freedom: (5-1)(2-1) = 4 p-value: The closest critical value on the chi square table with 4 degrees of freedom is 5.39 which has a tail probability of.25. Our computed test statistic is which gives an upper tail probability that is larger than.25. Thus, our p-value is larger than.25. Decision: Since p-value > α, we do not reject Ho. There is not enough evidence at the 5% level of significance to conclude that the shelf on which a cereal appears is dependent upon the manufacturer. 16. Of those cereals on the low shelf, what percentage is made by Nabisco? 2/21 =.95 = 9.5% 5

6 Use the multiple regression output below to answer the following questions. The output reflects the regression of the healthiness rating (Y) on the number of calories, fat, and fiber grams per serving as well as the shelf on which the cereal appears. SUMMARY OUTPUT: Regression using PredInt.xls Regression Statistics Multiple R.8284 R Square.6863 Adjusted R Square.6689 Standard Error Observations 77 ANOVA df SS MS F Significance (p-value) for F Regression Residual Total Dependent (Criterion) Variable: rating Coef-ficients Standard Error t Stat P-value (2-tails) Lower 95% Upper 95% X Values for Prediction Intercept calories fat fiber Shelf Confidence Level Prediction Interval for a Single Observation Predicted of rating, with the X Values that you Standard Error enter in the yellow boxes. Lower 95% Upper 95% Confidence Interval for Expected rating Fit while holding X constant at the values that you Standard Error enter in the yellow boxes. Lower 95% Upper 95% What is R 2? What does this value mean? This means that 68.63% of the observed variation in the healthiness ratings can be explained by the calories, fat, and fiber per serving in addition to the shelf on which the cereal appears. 18. Estimate the healthiness rating of a cereal with 1 calories, 2 grams of fat, grams of fiber per serving that appears on the low shelf. y ˆ = * * * 5.414*1 = Test to determine if the number of fat grams per serving is a significant linear predictor of the healthiness rating. State the null and alternative hypothesis, test statistic, p-value, decision and conclusion. Use α =.5. Ho: β = Ha: β 6

7 Test statistic: p-value:.2 Decision: Since p-value < α, reject Ho. There is enough evidence at the 5% level of significance to conclude that the number of fat grams is a significant linear predictor of the healthiness rating of breakfast cereals. 2. State and interpret the 95% confidence interval for estimating the population slope coefficient of the variable fiber. The 95% confidence interval is given by (1.455, 3.194). We are 95% confident that a one gram increase in fiber per serving gives an increase in the population average cereal rating of between and points when comparing cereals with the same number of calories and fat grams per serving that appear on the same shelf. 21. State and interpret the 95% confidence interval for estimating the population slope coefficient of the variable shelf. The 95% confidence interval is given by (-9.771, -1.58). When comparing cereals with the same number of calories, fat, and fiber per serving, cereals on the low shelf have a population average rating of between 1.58 and points lower than cereals on higher shelves. 22. Interpret the slope coefficient for the variable calories. For each additional calorie per serving contained in a breakfast cereal, the predicted average rating decreases by.337 points when comparing cereals with the same amount of fat and fiber per serving that appear on the same shelf in the grocery store. 7

### 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

### e = random error, assumed to be normally distributed with mean 0 and standard deviation σ

1 Linear Regression 1.1 Simple Linear Regression Model The linear regression model is applied if we want to model a numeric response variable and its dependency on at least one numeric factor variable.

### 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

### SOCI Homework 6 Key

SOCI 252-002 Homework 6 Key Professor François Nielsen Chapter 27 2. (pg. 702 drug use) a) The percentage of 9th graders in these countries who have used other drugs is estimated to have increased 0.615%

### " 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

### 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

### 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

### 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

### Null Hypothesis H 0. The null hypothesis (denoted by H 0

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

### Statistics 112 Regression Cheatsheet Section 1B - Ryan Rosario

Statistics 112 Regression Cheatsheet Section 1B - Ryan Rosario I have found that the best way to practice regression is by brute force That is, given nothing but a dataset and your mind, compute everything

### 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

### 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

### 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

### 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

### 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

### 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.

### 5. Linear Regression

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

### ACTM State Exam-Statistics

ACTM State Exam-Statistics For the 25 multiple-choice questions, make your answer choice and record it on the answer sheet provided. Once you have completed that section of the test, proceed to the tie-breaker

### 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

### Regression in ANOVA. James H. Steiger. Department of Psychology and Human Development Vanderbilt University

Regression in ANOVA James H. Steiger Department of Psychology and Human Development Vanderbilt University James H. Steiger (Vanderbilt University) 1 / 30 Regression in ANOVA 1 Introduction 2 Basic Linear

### 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

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

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

### 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

### Chapter Additional: Standard Deviation and Chi- Square

Chapter Additional: Standard Deviation and Chi- Square Chapter Outline: 6.4 Confidence Intervals for the Standard Deviation 7.5 Hypothesis testing for Standard Deviation Section 6.4 Objectives Interpret

### Seminar paper Statistics

Seminar paper Statistics The seminar paper must contain: - the title page - the characterization of the data (origin, reason why you have chosen this analysis,...) - the list of the data (in the table)

### 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

### where b is the slope of the line and a is the intercept i.e. where the line cuts the y axis.

Least Squares Introduction We have mentioned that one should not always conclude that because two variables are correlated that one variable is causing the other to behave a certain way. However, sometimes

### 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 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

### Descriptive Statistics

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

### Technology Step-by-Step Using StatCrunch

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

### 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

### 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

### Math 62 Statistics Sample Exam Questions

Math 62 Statistics Sample Exam Questions 1. (10) Explain the difference between the distribution of a population and the sampling distribution of a statistic, such as the mean, of a sample randomly selected

### 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

### Regression Analysis Prof. Soumen Maity Department of Mathematics Indian Institute of Technology, Kharagpur

Regression Analysis Prof. Soumen Maity Department of Mathematics Indian Institute of Technology, Kharagpur Lecture - 7 Multiple Linear Regression (Contd.) This is my second lecture on Multiple Linear Regression

### Simple Linear Regression in SPSS STAT 314

Simple Linear Regression in SPSS STAT 314 1. Ten Corvettes between 1 and 6 years old were randomly selected from last year s sales records in Virginia Beach, Virginia. The following data were obtained,

### Mean = (sum of the values / the number of the value) if probabilities are equal

Population Mean Mean = (sum of the values / the number of the value) if probabilities are equal Compute the population mean Population/Sample mean: 1. Collect the data 2. sum all the values in the population/sample.

### 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)

### 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

### 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

### Stats Review Chapters 3-4

Stats Review Chapters 3-4 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

### Introduction to Stata

Introduction to Stata September 23, 2014 Stata is one of a few statistical analysis programs that social scientists use. Stata is in the mid-range of how easy it is to use. Other options include SPSS,

### Regression III: Dummy Variable Regression

Regression III: Dummy Variable Regression Tom Ilvento FREC 408 Linear Regression Assumptions about the error term Mean of Probability Distribution of the Error term is zero Probability Distribution of

### 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

### Basic Statistcs Formula Sheet

Basic Statistcs Formula Sheet Steven W. ydick May 5, 0 This document is only intended to review basic concepts/formulas from an introduction to statistics course. Only mean-based procedures are reviewed,

### INCOME AND HAPPINESS 1. Income and Happiness

INCOME AND HAPPINESS 1 Income and Happiness Abstract Are wealthier people happier? The research study employed simple linear regression analysis to confirm the positive relationship between income and

### 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

### 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.

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

Open book and note Calculator OK Multiple Choice 1 point each MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data.

### The scatterplot indicates a positive linear relationship between waist size and body fat percentage:

STAT E-150 Statistical Methods Multiple Regression Three percent of a man's body is essential fat, which is necessary for a healthy body. However, too much body fat can be dangerous. For men between the

### c. The factor is the type of TV program that was watched. The treatment is the embedded commercials in the TV programs.

STAT E-150 - Statistical Methods Assignment 9 Solutions Exercises 12.8, 12.13, 12.75 For each test: Include appropriate graphs to see that the conditions are met. Use Tukey's Honestly Significant Difference

### 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

### 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

### 1 SAMPLE SIGN TEST. Non-Parametric Univariate Tests: 1 Sample Sign Test 1. A non-parametric equivalent of the 1 SAMPLE T-TEST.

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

### 1.5 Oneway Analysis of Variance

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

### BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394

BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394 1. Does vigorous exercise affect concentration? In general, the time needed for people to complete

### 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

### 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

### STATS8: Introduction to Biostatistics. Data Exploration. Babak Shahbaba Department of Statistics, UCI

STATS8: Introduction to Biostatistics Data Exploration Babak Shahbaba Department of Statistics, UCI Introduction After clearly defining the scientific problem, selecting a set of representative members

### SELF-TEST: SIMPLE REGRESSION

ECO 22000 McRAE SELF-TEST: SIMPLE REGRESSION Note: Those questions indicated with an (N) are unlikely to appear in this form on an in-class examination, but you should be able to describe the procedures

### AP Statistics 2002 Scoring Guidelines

AP Statistics 2002 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought

### 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

### Chapter 11: Linear Regression - Inference in Regression Analysis - Part 2

Chapter 11: Linear Regression - Inference in Regression Analysis - Part 2 Note: Whether we calculate confidence intervals or perform hypothesis tests we need the distribution of the statistic we will use.

### 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

### Box plots & t-tests. Example

Box plots & t-tests Box Plots Box plots are a graphical representation of your sample (easy to visualize descriptive statistics); they are also known as box-and-whisker diagrams. Any data that you can

### Chapter 2: Exploring Data with Graphs and Numerical Summaries. Graphical Measures- Graphs are used to describe the shape of a data set.

Page 1 of 16 Chapter 2: Exploring Data with Graphs and Numerical Summaries Graphical Measures- Graphs are used to describe the shape of a data set. Section 1: Types of Variables In general, variable can

### 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

### 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

### Section 7.1. Introduction to Hypothesis Testing. Schrodinger s cat quantum mechanics thought experiment (1935)

Section 7.1 Introduction to Hypothesis Testing Schrodinger s cat quantum mechanics thought experiment (1935) Statistical Hypotheses A statistical hypothesis is a claim about a population. Null hypothesis

### 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

### 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

### 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

### 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

### 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) -

### 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

### How Far is too Far? Statistical Outlier Detection

How Far is too Far? Statistical Outlier Detection Steven Walfish President, Statistical Outsourcing Services steven@statisticaloutsourcingservices.com 30-325-329 Outline What is an Outlier, and Why are

### 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,

### Simple Linear Regression One Binary Categorical Independent Variable

Simple Linear Regression Does sex influence mean GCSE score? In order to answer the question posed above, we want to run a linear regression of sgcseptsnew against sgender, which is a binary categorical

### Dongfeng Li. Autumn 2010

Autumn 2010 Chapter Contents Some statistics background; ; Comparing means and proportions; variance. Students should master the basic concepts, descriptive statistics measures and graphs, basic hypothesis

### 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

### MTH 140 Statistics Videos

MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative

### 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

### Multiple Regression in SPSS STAT 314

Multiple Regression in SPSS STAT 314 I. The accompanying data is on y = profit margin of savings and loan companies in a given year, x 1 = net revenues in that year, and x 2 = number of savings and loan

### MAT 118 DEPARTMENTAL FINAL EXAMINATION (written part) REVIEW. Ch 1-3. One problem similar to the problems below will be included in the final

MAT 118 DEPARTMENTAL FINAL EXAMINATION (written part) REVIEW Ch 1-3 One problem similar to the problems below will be included in the final 1.This table presents the price distribution of shoe styles offered

### Summary of Formulas and Concepts. Descriptive Statistics (Ch. 1-4)

Summary of Formulas and Concepts Descriptive Statistics (Ch. 1-4) Definitions Population: The complete set of numerical information on a particular quantity in which an investigator is interested. We assume

### 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

### 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

### 12: Analysis of Variance. Introduction

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

### Paired Differences and Regression

Paired Differences and Regression Students sometimes have difficulty distinguishing between paired data and independent samples when comparing two means. One can return to this topic after covering simple

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

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

### 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

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

Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing

### An example ANOVA situation. 1-Way ANOVA. Some notation for ANOVA. Are these differences significant? Example (Treating Blisters)

An example ANOVA situation Example (Treating Blisters) 1-Way ANOVA MATH 143 Department of Mathematics and Statistics Calvin College Subjects: 25 patients with blisters Treatments: Treatment A, Treatment

### 2. Filling Data Gaps, Data validation & Descriptive Statistics

2. Filling Data Gaps, Data validation & Descriptive Statistics Dr. Prasad Modak Background Data collected from field may suffer from these problems Data may contain gaps ( = no readings during this period)

### 0.1 Multiple Regression Models

0.1 Multiple Regression Models We will introduce the multiple Regression model as a mean of relating one numerical response variable y to two or more independent (or predictor variables. We will see different

### 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