# Solutions to Homework 10 Statistics 302 Professor Larget

 To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video
Save this PDF as:

Size: px
Start display at page:

## Transcription

2 Qtr 1 Qtr 2 Qtr 3 Qtr 4 OHL players % of Canadian births 23.7% 25.9% 25.9% 24.5% Let p 1, p 2, p 3, and p 4 be the proportion of hockey players born in the 1 st, 2 nd, 3 rd, and 4 th quarter of the year, respectively. We are testing H 0 : p 1 = 0.237, p 2 = 0.259, p 3 = and p 4 = H a : Some p i is not specified as inh 0 The total sample size is n = = 359. The expected counts are 359(0.237) = 85 for Qtr 1, 359(0.259) = 93 for Qtr 2, 359(0.259) = 93 for Qtr 3, and 359(0.245) = 88 for Qtr 4. The chi-square statistic is χ 2 = (147 85)2 85 (110 93)2 93 (52 93)2 93 (50 88)2 88 = We use the chi-square distribution with 4 1 = 3 degrees of freedom, which gives a very small p-value that is essentially zero. This is strong evidence that the distribution of birth dates for OHL hockey players differs significantly from the national proportions Can People Delay Death? (Graded for Completeness) A new study indicates that elderly people are able to postpone death for a short time to reach an important occasion. The researchers studied deaths from natural causes among 1200 elderly people of Chinese descent in California during six months before and after the Harbor Moon Festival. Thirty-three deaths occurred in the week before the Chinese festival, compared with an estimated deaths expected in that period. In the week following the festival, 70 deaths occurred, compared with an estimated 52. The numbers are so significant that is would be unlikely to occur by chance, said one of the researchers. (a) Given the information in the problem, is the χ 2 statistic likely to be relatively large or relatively small? (b) Is the p-value likely to be relatively large or relatively small? (c) In the week before the festival, which is higher: the observed count or the expected count? What does this tell us about the ability of elderly people to delay death? (d) What is the contribution to the χ 2 -statistic for the week before the festival? (e) In the week after the festival, which is higher: the observed count or the expected count? What does this tell us about the ability of elder people to delay death? (f) What is the contribution to the χ 2 -statistic for the week after the festival? (g) The researchers tell us that in a control group of elderly people in California who are not of Chinese descent, the same effect was not seen. Why did the researchers also include a control group? 2

3 (a) Since the results are given as statistically significant, the χ 2 -statistic is likely to be large. (b) Since the results are given as statistically significant, the p-value is likely to be small. (c) In the week before the festival, the expected count is higher than the observed count. This tells us that some elderly people may be able to delay death. (d) For the week before the festival, the contribution to the χ 2 statistic is (observed expected) 2 expected = (33?50.82) = (e) In the week after the festival, the observed count is higher than the expected count. This tells us that, although some elderly people are able to delay death, they don t delay it for very long. (f) For the week after the festival, the contribution to the χ 2 statistic is (observed expected) 2 expected = (70 52)2 52 = (g) The control group allows us to attribute the difference specifically to the meaningful event (the Harbor Moon Festival) since the effect was only seen in the group who found this event meaningful Metal Tags on Penguins (Graded for Completeness) In Exercise on page 403 we perform a test for the difference in the proportion of penguins who survive over a 10-year period, between penguins tagged with metal tags and those tagged with electronic tags. We are interested in testing whether the type of tag has an effect on penguin survival rate, this time using a chi-square test. In the study, 33 of the 167 metal-tagged penguins survived while 68 of the 189 electronic-tagged penguins survived. (a) Create a two-way table from the information given. (b) State the null and alternative hypotheses. (c) Give a table with the expected counts for each of the four categories. (d) Calculate the chi-square test statistic. (e) Determine the p-value and state the conclusion. (a) The two-way table of penguin survival vs type tag is shown: Metal Electronic Total Survived Died Total

4 (b) The hypothesis are H 0 : Type of tag is not related to survival H a : Type of tag is related to survival (c) The table below shows the expected counts, obtained for each cell by multiplying the row total by the column total and dividing by n = 356. Metal Electronic Survived Died d) We calculate the chi-square test statistic χ 2 = ( )2 ( ) = = 11.5 ( ) ( ) (e) We compare our test statistic of 11.5 from part (c) to a chi-square with 1 degree of freedom to get a p-value of There is strong evidence that the type of tag and survival rate of the penguins are related Favorite Skittles Flavor? (Graded for Accurateness) Exercise 7.13 on page 472 discusses a sample of people choosing their favorite Skittle flavor by color (green, orange, purple, red, or yellow). A separate poll sampled 91 people, again asking them their favorite skittle flavor, but rather than by color they asked by the actual flavor (lime, orange, grape, strawberry, and lemon, respectively). The table below shows the results from both polls. Does the way people choose their favorite Skittle type, by color or flavor, appear to be related to which type is chosen? (a) State the null and alternative hypotheses. (b) Give a table with the expected counts for each of the 10 cells. (c) Are the expected counts large enough for a chi-square test? (d) How many degrees of freedom do we have for this test? (e) Calculate the chi-square test statistic. (f) Determine the p-value. Do we find evidence that method of choice affects which is chosen? Green (Lime) Orange Purple (Grape) Red (Strawberry) Yellow (Lemon) Color Flavor (a) The hypotheses are H 0 : Skittles choice does not depend on method of choosing (color vs flavor) 4

6 results in the next table. Status \ Male Female Every day days/week days/week Every few weeks Less often Adding up all of these contributions, we obtain the χ 2 -statistic Using a chi-square distribution with df = (5 1) (2 1) = 4, we see that the p-value is This is very close to a 5% cutoff. At a 5% level, there is some evidence of a possible relationship between gender and frequency of status updates on Facebook. Females appear more likely to update their status at least once a day Laptop Computers and Sperm Count (Graded for Completeness) Studies have shown that heating the scrotum by just 1 C can reduce sperm count and sperm quality, with longterm consequences. Exercise on page 87 introduces a study indicating that males sitting with a laptop on their laps have increased scrotal temperatures. Does a lap pad help reduce the temperature increase? Does sitting with legs apart help? The study investigated all three of these conditions: legs together and a laptop computer on the lap, legs apart and a laptop computer on the lap, and legs together with a lap pad under the laptop computer. Scrotal temperature increase over a 60-minute session was measured in C, and the summary statistics are given in the table below. Condition n mean Std.Dev. Legs together Lap pad Legs apart (a) Which conditions has the largest mean temperature increase? Which has the smallest? (b) Do the data appear to satisfy the condition that the standard deviations are roughly the same? (The data satisfy the normality condition.) (c) Use the fact that sum of squares is 53.2 to test whether there is a difference in mean temperature increase between the three conditions. Show all details of the test, including an analysis of variance table. (a) Legs together with no lap pad has the largest temperature increase. Spreading the legs apart has the smallest temperature increase. (b) Yes, the standard deviations are similar. The largest, s 1 = 0.96, is not more than twice the smallest, s 3 =

7 (c) The null hypothesis is that the population mean temperature increases for the three conditions are all the same and the alternative hypothesis is that at least two of the means are different. We find the mean squares by dividing the sum of squares by the respective degrees of freedom (df = 3 1 = 2 for Groups, df = 87 3 = 84 for Error). The F-statistic is the ratio of the two mean squares. F = MSG MSE = = 10.9 These calculations are summarized in the ANOVA table below. Source DF SS MS F P Groups Error Total The p-value is the area above 10.9 in an F-distribution with numerator degrees of freedom 2 and denominator degrees of freedom 84. Using technology we see that the p-value= We reject H 0 and find strong evidence that average temperature increase is not the same for these three conditions. It appears that spreading legs apart may be more effective at reducing the temperature increase Sandwich Ants and Bread (Graded for Accurateness) Data 8.1 on page 492 describes an experiment to study how different sandwich fillings might affect the mean number of ants attracted to pieces of a sandwich. The students running this experiment also varied the type of break for the sandwiches, randomizing between four types: Multigrain, Rye, Wholemeal, and White. The ant counts in 6 trials and summary statistics for each type of break and the 24 trials as a whole are given in the table below and stored in SandwichAnts. Bread Ants Mean Std.Dev. Multigrain Rye Wholemeal White Total (a) Show how to use the summary information to compute the three sums of squares needed for using ANOVA to test for a difference in mean number of ants among these four types of bread. (b) Use the sums of squares from part (a) to construct the ANOVA table and complete the details for this test. Be sure to give a conclusion in the context of this data situation. (a) We find the required sum of squares using the shortcut formulas at the end of this section. We compare the group means to the overall mean: SSG = n i ( x i x) 2 = 6( ) 2 6( ) 2 6( ) 2 6( ) 2 =

8 We find the variability within the groups: SSE = (n i 1)s 2 i = (6 1) (6 1) (6 1) (6 1) = We find the total variability: SST otal = (n 1)s 2 = (24 1) = We see that SSG SSE = = The difference from SST otal = is due to rounding the means and standard deviations in the summary statistics. (b) We are testing vs H 0 : µ 1 = µ 2 = µ 3 = µ 4 H a : Some µ i µ j where the µ i s represent the mean numbers of ants for the four types of bread. We have 4 1 = 3 degrees of freedom for the groups, 24 4 = 20 degrees of freedom for the error, and 24 1 = 23 degrees of freedom for the total. We compute mean squares by dividing sums of squares by degrees of freedom, then take the ratio of the mean squares to compute the F-statistic. MSG = = MSE = The ANOVA table summarizing these calculations is shown below. = F = MSG MSE = = 0.27 Source DF SS MS F P Bread Error Total Using an F-distribution with 3 and 20 degrees of freedom, we find the area beyond F = 0.27 gives a p-value of This is a very large p-value, so we have no convincing evidence to conclude that the mean number of ants attracted to a sandwich depends on the type of bread. Computer Exercises For each R problem, turn in answers to questions with the written portion of the homework. Send the R code for the problem to Katherine Goode. The answers to questions in the written part should be well written, clear, and organized. The R code should be commented and well formatted. R problem 1 (Graded for Accurateness) The function chisq.test() can be used for chisquare tests. For goodness-of-fit tests, provide a single array of counts and an optional array of the same length of probabilities for each case. (R uses uniform probabilities by default.) For example, in class for the Rock, Paper, Scissors data, we had total counts of 88, 74, and 66. Here is an example. chisq.test(c(88, 74, 66), p = c(1, 1, 1)/3) ## 8

9 ## Chi-squared test for given probabilities ## ## data: c(88, 74, 66) ## X-squared = 3.263, df = 2, p-value = Use chisq.test() for the data in Exercise 7.14 and compare to your previous answer. Using R, we get the following output. Chi-squared test for given probabilities data: c(66, 39, 14) X-squared = , df = 2, p-value = 3.936e-08 We find that our p-value is very close to 0, which agrees with the p-value found in Exercise The following code in R was used to get this value. chisq.test(c(66, 39, 14), p = c(1, 1, 1)/3) 2. Using the same data, test if the data is consistent with the null distribution p rock = 0.5, p paper = 0.3, p scissors = 0.2. With this new null distribution, we get the following output from R. Chi-squared test for given probabilities data: c(66, 39, 14) X-squared = , df = 2, p-value = We see that our p-value is not significant at the 0.05 confidence level. Thus, there is no evidence to support the fact that the data is not consistent with the null distribution of p rock = 0.5, p paper = 0.3, p scissors = 0.2. The following code in R was used to get this value. chisq.test(c(66, 39, 14), p = c(0.5, 0.3,0.2)) 3. A randomization distribution method can also be used to calculate a p-value. Add the argument simulate.p.value=true to the call to chisq.test() with B=10000 and compare answer to that in the first part. chisq.test(c(66, 39, 14), simulate.p.value = TRUE, B = 10000) We get the following output from R. 9

10 Chi-squared test for given probabilities with simulated p-value (based on replicates) data: c(66, 39, 14) X-squared = , df = NA, p-value = 9.999e-05 The p-value is also close to 0 in this case. The following R code was used to obtain this value. chisq.test(c(66, 39, 14), simulate.p.value = TRUE, B = 10000) R Problem 2 (Graded for Accurateness) Here you will learn to use chisq.test() for tests of association where the counts are in matrices. Compare the answer you get with this function with the answer from your hand calculation on Exercise x = matrix(c(18, 13, 9, 16, 15, 19, 13, 34, 11, 9), nrow = 2, ncol = 5) chisq.test(x) Using this code, we get the following output from R. Pearson s Chi-squared test data: x X-squared = , df = 4, p-value = We see that the p-value of matches the p-value of found in the hand calculation of Exercise

### 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

### One-Way Analysis of Variance: A Guide to Testing Differences Between Multiple Groups

One-Way Analysis of Variance: A Guide to Testing Differences Between Multiple Groups In analysis of variance, the main research question is whether the sample means are from different populations. The

### 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

### 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

### STATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4

STATISTICS 8, FINAL EXAM NAME: KEY Seat Number: Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 Make sure you have 8 pages. You will be provided with a table as well, as a separate

### Math 58. Rumbos Fall 2008 1. Solutions to Review Problems for Exam 2

Math 58. Rumbos Fall 2008 1 Solutions to Review Problems for Exam 2 1. For each of the following scenarios, determine whether the binomial distribution is the appropriate distribution for the random variable

### Chapter 7. One-way ANOVA

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

### Solutions to Homework 6 Statistics 302 Professor Larget

s to Homework 6 Statistics 302 Professor Larget Textbook Exercises 5.29 (Graded for Completeness) What Proportion Have College Degrees? According to the US Census Bureau, about 27.5% of US adults over

### Statistical Functions in Excel

Statistical Functions in Excel There are many statistical functions in Excel. Moreover, there are other functions that are not specified as statistical functions that are helpful in some statistical analyses.

### 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

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

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

### Chapter 19 The Chi-Square Test

Tutorial for the integration of the software R with introductory statistics Copyright c Grethe Hystad Chapter 19 The Chi-Square Test In this chapter, we will discuss the following topics: We will plot

### Elementary Statistics

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

### Normality Testing in Excel

Normality Testing 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

### CHAPTER IV FINDINGS AND CONCURRENT DISCUSSIONS

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

### WISE Power Tutorial All Exercises

ame Date Class WISE Power Tutorial All Exercises Power: The B.E.A.. Mnemonic Four interrelated features of power can be summarized using BEA B Beta Error (Power = 1 Beta Error): Beta error (or Type II

### 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:

### International Statistical Institute, 56th Session, 2007: Phil Everson

Teaching Regression using American Football Scores Everson, Phil Swarthmore College Department of Mathematics and Statistics 5 College Avenue Swarthmore, PA198, USA E-mail: peverso1@swarthmore.edu 1. Introduction

### 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

### 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

### 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

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

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

### Chi Square Distribution

17. Chi Square A. Chi Square Distribution B. One-Way Tables C. Contingency Tables D. Exercises Chi Square is a distribution that has proven to be particularly useful in statistics. The first section describes

### Unit 31: One-Way ANOVA

Unit 31: One-Way ANOVA Summary of Video A vase filled with coins takes center stage as the video begins. Students will be taking part in an experiment organized by psychology professor John Kelly in which

### 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 F distribution and the basic principle behind ANOVAs. Situating ANOVAs in the world of statistical tests

Tutorial The F distribution and the basic principle behind ANOVAs Bodo Winter 1 Updates: September 21, 2011; January 23, 2014; April 24, 2014; March 2, 2015 This tutorial focuses on understanding rather

: Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 Sigma-Restricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 Summary

### 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

### Assessing Measurement System Variation

Assessing Measurement System Variation Example 1: Fuel Injector Nozzle Diameters Problem A manufacturer of fuel injector nozzles installs a new digital measuring system. Investigators want to determine

### In the past, the increase in the price of gasoline could be attributed to major national or global

Chapter 7 Testing Hypotheses Chapter Learning Objectives Understanding the assumptions of statistical hypothesis testing Defining and applying the components in hypothesis testing: the research and null

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

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

### ANOVA. February 12, 2015

ANOVA February 12, 2015 1 ANOVA models Last time, we discussed the use of categorical variables in multivariate regression. Often, these are encoded as indicator columns in the design matrix. In [1]: %%R

### CHAPTER 12. Chi-Square Tests and Nonparametric Tests LEARNING OBJECTIVES. USING STATISTICS @ T.C. Resort Properties

CHAPTER 1 Chi-Square Tests and Nonparametric Tests USING STATISTICS @ T.C. Resort Properties 1.1 CHI-SQUARE TEST FOR THE DIFFERENCE BETWEEN TWO PROPORTIONS (INDEPENDENT SAMPLES) 1. CHI-SQUARE TEST FOR

### 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

### 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

### An analysis method for a quantitative outcome and two categorical explanatory variables.

Chapter 11 Two-Way ANOVA An analysis method for a quantitative outcome and two categorical explanatory variables. If an experiment has a quantitative outcome and two categorical explanatory variables that

### Example Research Scenarios

Example Research Scenarios In this document, I've collected many of the scenario problems that we discussed in class throughout the semester. For each problem you should: a) Identify the most appropriate

### 4.1 Exploratory Analysis: Once the data is collected and entered, the first question is: "What do the data look like?"

Data Analysis Plan The appropriate methods of data analysis are determined by your data types and variables of interest, the actual distribution of the variables, and the number of cases. Different analyses

### A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

CHAPTER 5. A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING 5.1 Concepts When a number of animals or plots are exposed to a certain treatment, we usually estimate the effect of the treatment

### 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

### 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

### Chapter 9. Two-Sample Tests. Effect Sizes and Power Paired t Test Calculation

Chapter 9 Two-Sample Tests Paired t Test (Correlated Groups t Test) Effect Sizes and Power Paired t Test Calculation Summary Independent t Test Chapter 9 Homework Power and Two-Sample Tests: Paired Versus

### 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

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

ANOVA ANOVA Analysis of Variance Chapter 6 A procedure for comparing more than two groups independent variable: smoking status non-smoking one pack a day > two packs a day dependent variable: number of

### IBM SPSS Statistics for Beginners for Windows

ISS, NEWCASTLE UNIVERSITY IBM SPSS Statistics for Beginners for Windows A Training Manual for Beginners Dr. S. T. Kometa A Training Manual for Beginners Contents 1 Aims and Objectives... 3 1.1 Learning

### Indices of Model Fit STRUCTURAL EQUATION MODELING 2013

Indices of Model Fit STRUCTURAL EQUATION MODELING 2013 Indices of Model Fit A recommended minimal set of fit indices that should be reported and interpreted when reporting the results of SEM analyses:

### 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

### Session 8 Probability

Key Terms for This Session Session 8 Probability Previously Introduced frequency New in This Session binomial experiment binomial probability model experimental probability mathematical probability outcome

### 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

### Soci252-002 Data Analysis in Sociological Research. Homework 5 Computer Handout

University of North Carolina Chapel Hill Soci252-002 Data Analysis in Sociological Research Spring 2013 Professor François Nielsen Homework 5 Computer Handout Readings This handout covers computer issues

### ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R.

ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. 1. Motivation. Likert items are used to measure respondents attitudes to a particular question or statement. One must recall

### 15.075 Exam 4. Instructor: Cynthia Rudin TA: Dimitrios Bisias. December 21, 2011

15.075 Exam 4 Instructor: Cynthia Rudin TA: Dimitrios Bisias December 21, 2011 Grading is based on demonstration of conceptual understanding, so you need to show all of your work. Problem 1 Choose Y or

### Introduction to Statistics and Quantitative Research Methods

Introduction to Statistics and Quantitative Research Methods Purpose of Presentation To aid in the understanding of basic statistics, including terminology, common terms, and common statistical methods.

### Introduction to. Hypothesis Testing CHAPTER LEARNING OBJECTIVES. 1 Identify the four steps of hypothesis testing.

Introduction to Hypothesis Testing CHAPTER 8 LEARNING OBJECTIVES After reading this chapter, you should be able to: 1 Identify the four steps of hypothesis testing. 2 Define null hypothesis, alternative

### Survey, Statistics and Psychometrics Core Research Facility University of Nebraska-Lincoln. Log-Rank Test for More Than Two Groups

Survey, Statistics and Psychometrics Core Research Facility University of Nebraska-Lincoln Log-Rank Test for More Than Two Groups Prepared by Harlan Sayles (SRAM) Revised by Julia Soulakova (Statistics)

Table of Contents Preface Chapter 1: Introduction 1-1 Opening an SPSS Data File... 2 1-2 Viewing the SPSS Screens... 3 o Data View o Variable View o Output View 1-3 Reading Non-SPSS Files... 6 o Convert

### 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

### SPSS Manual for Introductory Applied Statistics: A Variable Approach

SPSS Manual for Introductory Applied Statistics: A Variable Approach John Gabrosek Department of Statistics Grand Valley State University Allendale, MI USA August 2013 2 Copyright 2013 John Gabrosek. All

### 5 Cumulative Frequency Distributions, Area under the Curve & Probability Basics 5.1 Relative Frequencies, Cumulative Frequencies, and Ogives

5 Cumulative Frequency Distributions, Area under the Curve & Probability Basics 5.1 Relative Frequencies, Cumulative Frequencies, and Ogives We often have to compute the total of the observations in a

### Sam Schaefer April 2011

Football Betting Trends Sam Schaefer April 2011 2 Acknowledgements I would like to take this time to thank all of those who have contributed to my learning the past four years. This includes my parents,

### 3. There are three senior citizens in a room, ages 68, 70, and 72. If a seventy-year-old person enters the room, the

TMTA Statistics Exam 2011 1. Last month, the mean and standard deviation of the paychecks of 10 employees of a small company were \$1250 and \$150, respectively. This month, each one of the 10 employees

### Northumberland Knowledge

Northumberland Knowledge Know Guide How to Analyse Data - November 2012 - This page has been left blank 2 About this guide The Know Guides are a suite of documents that provide useful information about

### HOW TO WRITE A LABORATORY REPORT

HOW TO WRITE A LABORATORY REPORT Pete Bibby Dept of Psychology 1 About Laboratory Reports The writing of laboratory reports is an essential part of the practical course One function of this course is to

### Guide to Microsoft Excel for calculations, statistics, and plotting data

Page 1/47 Guide to Microsoft Excel for calculations, statistics, and plotting data Topic Page A. Writing equations and text 2 1. Writing equations with mathematical operations 2 2. Writing equations with

### Simple Predictive Analytics Curtis Seare

Using Excel to Solve Business Problems: Simple Predictive Analytics Curtis Seare Copyright: Vault Analytics July 2010 Contents Section I: Background Information Why use Predictive Analytics? How to use

### 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

### Appendix 2 Statistical Hypothesis Testing 1

BIL 151 Data Analysis, Statistics, and Probability By Dana Krempels, Ph.D. and Steven Green, Ph.D. Most biological measurements vary among members of a study population. These variations may occur for

### Statistical Models in R

Statistical Models in R Some Examples Steven Buechler Department of Mathematics 276B Hurley Hall; 1-6233 Fall, 2007 Outline Statistical Models Structure of models in R Model Assessment (Part IA) Anova

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

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

There are three kinds of people in the world those who are good at math and those who are not. PSY 511: Advanced Statistics for Psychological and Behavioral Research 1 Positive Views The record of a month

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

MONT 07N Understanding Randomness Solutions For Final Examination May, 00 Short Answer (a) (0) How are the EV and SE for the sum of n draws with replacement from a box computed? Solution: The EV is n times

### PERCEPTION OF SENIOR CITIZEN RESPONDENTS AS TO REVERSE MORTGAGE SCHEME

CHAPTER- V PERCEPTION OF SENIOR CITIZEN RESPONDENTS AS TO REVERSE MORTGAGE SCHEME 5.1 Introduction The present study intended to investigate the senior citizen s retirement planning and their perception

### High School Statistics and Probability Common Core Sample Test Version 2

High School Statistics and Probability Common Core Sample Test Version 2 Our High School Statistics and Probability sample test covers the twenty most common questions that we see targeted for this level.

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

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

### Whitney Colbert Research Methods for the Social Sciences Trinity College Spring 2012

ALCOHOL IN COLLEGE ATHLETICS: THE FIGHT TO RAISE AWARENESS OF BINGE DRINKING ON COLLEGE ATHLETIC TEAMS Whitney Colbert Research Methods for the Social Sciences Trinity College Spring 2012 While there is

### ESTIMATION OF THE EFFECTIVE DEGREES OF FREEDOM IN T-TYPE TESTS FOR COMPLEX DATA

m ESTIMATION OF THE EFFECTIVE DEGREES OF FREEDOM IN T-TYPE TESTS FOR COMPLEX DATA Jiahe Qian, Educational Testing Service Rosedale Road, MS 02-T, Princeton, NJ 08541 Key Words" Complex sampling, NAEP data,

### Unit 26: Small Sample Inference for One Mean

Unit 26: Small Sample Inference for One Mean Prerequisites Students need the background on confidence intervals and significance tests covered in Units 24 and 25. Additional Topic Coverage Additional coverage

### 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) -

### Use of deviance statistics for comparing models

A likelihood-ratio test can be used under full ML. The use of such a test is a quite general principle for statistical testing. In hierarchical linear models, the deviance test is mostly used for multiparameter

### Solutions to Homework 3 Statistics 302 Professor Larget

s to Homework 3 Statistics 302 Professor Larget Textbook Exercises 3.20 Customized Home Pages A random sample of n = 1675 Internet users in the US in January 2010 found that 469 of them have customized

### Violent crime total. Problem Set 1

Problem Set 1 Note: this problem set is primarily intended to get you used to manipulating and presenting data using a spreadsheet program. While subsequent problem sets will be useful indicators of the

### Factor Analysis. Principal components factor analysis. Use of extracted factors in multivariate dependency models

Factor Analysis Principal components factor analysis Use of extracted factors in multivariate dependency models 2 KEY CONCEPTS ***** Factor Analysis Interdependency technique Assumptions of factor analysis

### PSYC 381 Statistics Arlo Clark-Foos, Ph.D.

One-Way Within- Groups ANOVA PSYC 381 Statistics Arlo Clark-Foos, Ph.D. Comparing Designs Pros of Between No order or carryover effects Between-Groups Design Pros of Within More costly Higher variability

### Testing a Hypothesis about Two Independent Means

1314 Testing a Hypothesis about Two Independent Means How can you test the null hypothesis that two population means are equal, based on the results observed in two independent samples? Why can t you use

### Introduction to Statistics with GraphPad Prism (5.01) Version 1.1

Babraham Bioinformatics Introduction to Statistics with GraphPad Prism (5.01) Version 1.1 Introduction to Statistics with GraphPad Prism 2 Licence This manual is 2010-11, Anne Segonds-Pichon. This manual

### Biostatistics: Types of Data Analysis

Biostatistics: Types of Data Analysis Theresa A Scott, MS Vanderbilt University Department of Biostatistics theresa.scott@vanderbilt.edu http://biostat.mc.vanderbilt.edu/theresascott Theresa A Scott, MS

### Introduction to Estimation

10. Estimation A. Introduction B. Degrees of Freedom C. Characteristics of Estimators D. Confidence Intervals 1. Introduction 2. Confidence Interval for the Mean 3. t distribution 4. Confidence Interval

### Two-Way Tables. Lesson 16. Main Idea. New Vocabulary two-way table relative frequency

Lesson 16 Main Idea Construct and interpret two-way tables. New Vocabulary two-way table relative frequency Math Online glencoe.com Two-Way Tables SCHOOL The data from a survey of 50 students is shown

### An introduction to using Microsoft Excel for quantitative data analysis

Contents An introduction to using Microsoft Excel for quantitative data analysis 1 Introduction... 1 2 Why use Excel?... 2 3 Quantitative data analysis tools in Excel... 3 4 Entering your data... 6 5 Preparing

### Pearson Student Mobile Device Survey 2015

Pearson Student Mobile Device Survey 2015 National Report: College Students Report date: Revised June, 2015 Conducted by Harris Poll This report contains public findings Table of Contents Background &

### 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

### 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

### www.rmsolutions.net R&M Solutons

Ahmed Hassouna, MD Professor of cardiovascular surgery, Ain-Shams University, EGYPT. Diploma of medical statistics and clinical trial, Paris 6 university, Paris. 1A- Choose the best answer The duration

### 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.

### Survey Research Data Analysis

Survey Research Data Analysis Overview Once survey data are collected from respondents, the next step is to input the data on the computer, do appropriate statistical analyses, interpret the data, and

### Advanced Statistical Analysis of Mortality. Rhodes, Thomas E. and Freitas, Stephen A. MIB, Inc. 160 University Avenue. Westwood, MA 02090

Advanced Statistical Analysis of Mortality Rhodes, Thomas E. and Freitas, Stephen A. MIB, Inc 160 University Avenue Westwood, MA 02090 001-(781)-751-6356 fax 001-(781)-329-3379 trhodes@mib.com Abstract

### Students' Opinion about Universities: The Faculty of Economics and Political Science (Case Study)

Cairo University Faculty of Economics and Political Science Statistics Department English Section Students' Opinion about Universities: The Faculty of Economics and Political Science (Case Study) Prepared