# Stat1600 Solution to Midterm #2 Form A

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Stat1600 Solution to Midterm #2 Form A 1. (10 points) According to the Centers for Disease Control and Prevention, 33.5% U.S. adults have high LDL, or bad, cholestrol. Given a random sample of n=12 U.S. adults, what is the probability that exactly 2 adults have high LDL. P (X= 2) = 12! 2!(12 2)! (.335)2 (1.335) 12 2 = ! (.335) 2 (.665) ! = (.335)2 (.665) 10 = 66 (.335) 2 (.665) 10 = According to a recent population survey, 24.7% of the State of Michigan population 25 years old and over have completed a bachelor s degree. Given a random sample of 100 persons in Michigan 25 years old or over, (a) (10 points) the number of persons who have completed a bachelor s degree is expected to be around, give or take or so. µ = np = = 24.7; σ = npq = 24.7 (1.247) = = The number of people who have completed a bachelor s degree is expected to be around 24.7, give or take (b) (10 points) what is the probability that out of the sample of n=100 that 27 or more have completed a bachelors degree? (Hint: Use the normal approximation of the binomial.) 1

2 P (X 27) = P (X > 26.5) ( ) P Z > = P (Z > 0.42) P (Z 0.42) = = = = = z z 3. According to Larsen, R. J., and Marx, M. L. (1986). An Introduction to Mathematical Statistics and Its Applications. Second Edition. Prentice-Hall, Englewood Cliffs, New Jersey, page 295: There is a theory that the anticipation of a birthday can prolong a person s life. In a study set up to examine that notion statistically, it was found that only 60 of 747 people whose obituaries were published in Salt Lake City in 1975 died in the three-month period preceding their birthday. (a) (10 points) What percentage of people in Salt Lake City in 1975 died in the threemonth period preceding their birthday? ˆp = = 0.08 i.e., 8%. (b) (10 points) Calculate the standard error for your estimate in (a) (1 0.08) SE = = i.e., 1.0%. 747 (c) (10 points) Calculate a 95% confidence interval for the true percentage. 2

3 ME = 1.96SE = = A 95% confidence interval for the true proportion is ( , ) = (0.060, 0.100). Hence a 95% confidence interval for the true percentage is (6.0%, 10.0%). 4. The table below shows the result of a study of the effectiveness of thalidomide in healing mouth ulcers in AIDS patients (an announcement by the National Institutes of Health on October 31, 1995): ulcers healed? YES NO Treatment 14 9 Placebo 1 21 (a) (10 points) Estimate the difference in heal rates (i.e., difference in proportions) of the two groups (Treatment versus Placebo). Let group 1 = Treatment and group 2 = Placebo. Then n 1 = = 23; n 2 = = 22. It follows ˆp 1 = = 0.609; ˆp 2 = 1 22 = The difference in proportions is estimated by ˆp 1 ˆp 2 = = (b) (10 points) Calculate a 95% confidence interval for the difference in heal rates. Does the interval exclude 0? Is the difference statistically significant? ANSWER (show your work): 3

4 From part (a), we can calculate the standard error of the estimated difference in proportions:.609 (1.609).045 (1.045) SE = = = =.111 Hence the margin of error is ME = =.218. Consequently, we can get a 95% c.i. for p 1 p 2 : ( , ) = (0.346, 0.782) which excludes 0. Therefore, the proportions differ and it appears that the heal rate for the Treatment group is greater than that of the Placebo group. Note that the interpretation of this 95% confidence interval: we are 95% confident that the difference in proportions (percentages) is in between (34.6%) and and (78.2%). ulcers healed? YES NO Treatment 14 9 Placebo 1 21 (c) (10 points) Estimate the odds ratio of those who were healed (YES) in the two groups. Interpret your answer in words. The odds ratio is estimated as OR = odds 1 odds 2 = 14/9 1/21 = That is, the odds for those in the Treatment group to be healed is 32.7 times as high as that for those in the Placebo group. (d) (10 points) Estimate the ratio of proportions of those who were healed (YES) in the two groups. Interpret your answer in words. 4

5 The ratio of heal rates is estimated as RR = ˆp 1 ˆp 2 = = 13.5 That is, those in the Treatment group are 13.5 times more likely to be healed than those in the Placebo group. 5. EXTRA CREDIT PROBLEM. (5 points) In the past, numerous epidemiological studies showed that women who were taking combined Hormone Replacement Therapy (HRT) also had a lower-than-average incidence of Coronary Heart Disease (CHD), leading doctors to propose that HRT was protective against CHD. Certainly, the claim was false. List at least two possible confounders and pick one of them to show the pathway graph that connects the confounder, HRT, and CHD. (Source: Wikipedia) There exist possible confounders that could be probable causes to the lower-thanaverage incidence of CHD. For instance, higher socio-economic status and better nutrition. A possible pathway could be higher socio-economic status = lower CHD taking HRT 5

### Stat1600 Midterm #2 Solution to Form A

Stat1600 Midterm #2 Solution to Form A 1. Of 100 adults selected randomly from one town, 64 have health insurance. A researcher wants to construct a 95% confidence interval for the percentage of all adults

### Today s lecture. Lecture 6: Dichotomous Variables & Chi-square tests. Proportions and 2 2 tables. How do we compare these proportions

Today s lecture Lecture 6: Dichotomous Variables & Chi-square tests Sandy Eckel seckel@jhsph.edu Dichotomous Variables Comparing two proportions using 2 2 tables Study Designs Relative risks, odds ratios

### Review the following from Chapter 5

Bluman, Chapter 6 1 Review the following from Chapter 5 A surgical procedure has an 85% chance of success and a doctor performs the procedure on 10 patients, find the following: a) The probability that

### Correlation study > prove cause and effect relationship. a) hours spent practicing at a golf driving range, golf drive distance

Cause and Effect identification of causal relationships, or proving that a particular independent variable (the cause) has an effect on the dependent variable of interest (the effect). Correlation study

### Page 548, Exercise 13

Millersville University Name Answer Key Department of Mathematics MATH 130, Elements of Statistics I, Homework 4 April 29, 2008 Page 548, Exercise 13 Height versus Arm Span A statistics student believes

### Lesson 14 14 Outline Outline

Lesson 14 Confidence Intervals of Odds Ratio and Relative Risk Lesson 14 Outline Lesson 14 covers Confidence Interval of an Odds Ratio Review of Odds Ratio Sampling distribution of OR on natural log scale

### Math 140: Introductory Statistics Instructor: Julio C. Herrera Exam 3 January 30, 2015

Name: Exam Score: Instructions: This exam covers the material from chapter 7 through 9. Please read each question carefully before you attempt to solve it. Remember that you have to show all of your work

### Question 1 Question 2 Question 3 Question 4 Question 5 Question 6. Math 144 tutorial April, 2010

Math 144 tutorial 7 12 April, 2010 1. Let us define S 2 = 1 n n i=1 (X i X) 2. Show that E(S 2 ) = n 1 n σ2. 1. Let us define S 2 = 1 n n i=1 (X i X) 2. Show that E(S 2 ) = n 1 n σ2. 1. Let us define S

### HYPOTHESIS TESTING (TWO SAMPLE) - CHAPTER 8 1. how can a sample be used to estimate the unknown parameters of a population

HYPOTHESIS TESTING (TWO SAMPLE) - CHAPTER 8 1 PREVIOUSLY estimation how can a sample be used to estimate the unknown parameters of a population use confidence intervals around point estimates of central

### STAT 5817: Logistic Regression and Odds Ratio

A cohort of people is a group of people whose membership is clearly defined. A prospective study is one in which a cohort of people is followed for the occurrence or nonoccurrence of specified endpoints

### ACTM Regional Statistics Multiple Choice Questions

ACTM Regional Statistics Multiple Choice Questions This exam includes 2 multiple- choice items and three constructed- response items that may be used as tie- breakers. Record your answer to each of the

### Confidence Intervals about a Population Mean

Confidence Intervals about a Population Mean MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2015 Motivation Goal: to estimate a population mean µ based on data collected

### Size of a study. Chapter 15

Size of a study 15.1 Introduction It is important to ensure at the design stage that the proposed number of subjects to be recruited into any study will be appropriate to answer the main objective(s) of

### Stat 371, Cecile Ane Practice problems Midterm #2, Spring 2012

Stat 371, Cecile Ane Practice problems Midterm #2, Spring 2012 The first 3 problems are taken from previous semesters exams, with solutions at the end of this document. The other problems are suggested

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

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

Goals of This Course Be able to understand a study design (very basic concept) Be able to understand statistical concepts in a medical paper Be able to perform a data analysis Understanding: PECO study

### Determining the Sample Size: One Sample

Sample Sie Laboratory Determining the Sample Sie: One Sample OVERVIEW In this lab, you will be determining the sample sie for population means and population proportions. This lab is intended to help you

### Sampling Central Limit Theorem Proportions. Outline. 1 Sampling. 2 Central Limit Theorem. 3 Proportions

Outline 1 Sampling 2 Central Limit Theorem 3 Proportions Outline 1 Sampling 2 Central Limit Theorem 3 Proportions Populations and samples When we use statistics, we are trying to find out information about

### 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

### Epidemiology. Learning Objectives

Epidemiology David G. Weismiller, MD, ScM, FAAFP Professor Department of Family Medicine The rody School of Medicine at East Carolina University Greenville, North Carolina Learning Objectives 1. Explain

### Confidence Intervals for the Area Under an ROC Curve

Chapter 261 Confidence Intervals for the Area Under an ROC Curve Introduction Receiver operating characteristic (ROC) curves are used to assess the accuracy of a diagnostic test. The technique is used

### Review for Exam 2. H 0 : p 1 p 2 = 0 H A : p 1 p 2 0

Review for Exam 2 1 Time in the shower The distribution of the amount of time spent in the shower (in minutes) of all Americans is right-skewed with mean of 8 minutes and a standard deviation of 10 minutes.

### Let X the gain for the company( per package ) Question 2

DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS Stat240, J.Jeneralczuk. EXAM 2 - practice exam NAME: Discussion session #: Chapter 5 Question 1 From past experience, a shipping company

### Test 12 Tests of Significance Homework Part 1 (Chpts & 11.2)

Name Period Test 12 Tests of Significance Homework Part 1 (Chpts. 12.2 & 11.2) 1. School officials are interested in implementing a policy that would allow students to bring their own technology to school

### Power and Sample Size Determination

Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 Power 1 / 31 Experimental Design To this point in the semester,

### Confidence Intervals and Hypothesis Testing

Name: Class: Date: Confidence Intervals and Hypothesis Testing Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The librarian at the Library of Congress

### STATISTICS 151 SECTION 1 FINAL EXAM MAY

STATISTICS 151 SECTION 1 FINAL EXAM MAY 2 2009 This is an open book exam. Course text, personal notes and calculator are permitted. You have 3 hours to complete the test. Personal computers and cellphones

### PHP 2510 Central limit theorem, confidence intervals. PHP 2510 October 20,

PHP 2510 Central limit theorem, confidence intervals PHP 2510 October 20, 2008 1 Distribution of the sample mean Case 1: Population distribution is normal For an individual in the population, X i N(µ,

### Estimating a population proportion

Introductory Statistics Lectures Estimating a population proportion Confidence intervals for proportions Department of Mathematics Pima Community College Redistribution of this material is prohibited without

### Logistic Regression: Basics

Evidence is no evidence if based solely on p value Logistic Regression: Basics Prediction Model: Binary Outcomes Nemours Stats 101 Laurens Holmes, Jr. General Linear Model OUTCOME Continuous Counts Data

### Statistics - Written Examination MEC Students - BOVISA

Statistics - Written Examination MEC Students - BOVISA Prof.ssa A. Guglielmi 26.0.2 All rights reserved. Legal action will be taken against infringement. Reproduction is prohibited without prior consent.

### UCLA STAT 13 Statistical Methods - Final Exam Review Solutions Chapter 7 Sampling Distributions of Estimates

UCLA STAT 13 Statistical Methods - Final Exam Review Solutions Chapter 7 Sampling Distributions of Estimates 1. (a) (i) µ µ (ii) σ σ n is exactly Normally distributed. (c) (i) is approximately Normally

### Relative Risk, Odds, and Fisher s exact test

Relative Risk, Odds, and Fisher s exact test I) Relative Risk A) Simply, relative risk is the ratio of p 1 / p 2. For instance, suppose we wanted to take another look at our Seat belt safety data from

### Chapter 11: Two Variable Regression Analysis

Department of Mathematics Izmir University of Economics Week 14-15 2014-2015 In this chapter, we will focus on linear models and extend our analysis to relationships between variables, the definitions

### Hormone Replacement Therapy : The New Debate. Susan T. Hingle, M.D.

Hormone Replacement Therapy : The New Debate Susan T. Hingle, M.D. Background Hormone replacement therapy (HRT) is extensively used in the United States, especially for: *treatment of menopausal symptoms

### C. The null hypothesis is not rejected when the alternative hypothesis is true. A. population parameters.

Sample Multiple Choice Questions for the material since Midterm 2. Sample questions from Midterms and 2 are also representative of questions that may appear on the final exam.. A randomly selected sample

### 6.1 The Elements of a Test of Hypothesis

University of California, Davis Department of Statistics Summer Session II Statistics 13 August 22, 2012 Date of latest update: August 20 Lecture 6: Tests of Hypothesis Suppose you wanted to determine

### I. Basics of Hypothesis Testing

Introduction to Hypothesis Testing This deals with an issue highly similar to what we did in the previous chapter. In that chapter we used sample information to make inferences about the range of possibilities

### Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 8.1 Homework Answers

Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 8.1 Homework Answers 8.1 In each of the following circumstances state whether you would use the large sample confidence interval,

### Lecture Topic 6: Chapter 9 Hypothesis Testing

Lecture Topic 6: Chapter 9 Hypothesis Testing 9.1 Developing Null and Alternative Hypotheses Hypothesis testing can be used to determine whether a statement about the value of a population parameter should

### Point and Interval Estimates

Point and Interval Estimates Suppose we want to estimate a parameter, such as p or µ, based on a finite sample of data. There are two main methods: 1. Point estimate: Summarize the sample by a single number

### Chapter 7. Hypothesis Testing with One Sample

Chapter 7 Hypothesis Testing with One Sample 7.1 Introduction to Hypothesis Testing Hypothesis Tests A hypothesis test is a process that uses sample statistics to test a claim about the value of a population

### Cholesterol Treatment Trialists (CTT) Collaboration. Slide deck

Cholesterol Treatment Trialists (CTT) Collaboration Slide deck CTT Collaboration: Background* History: Founded in 1993 (prior to publication of 4S trial in 1994) Original protocol published in 1995 Trial

### Study Design & Methodology

UNIVERSITY of LIMERICK OLLSCOIL LUIMNIGH STATISTICAL CONSULTING UNIT Research in Health Sciences Study Design & Methodology Study Design & Methodology Dr Jean Saunders C.Stat Inc extra Declan slides Lyons

### Chapter 8. Hypothesis Testing

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

### Biostatistics Lab Notes

Biostatistics Lab Notes Page 1 Lab 1: Measurement and Sampling Biostatistics Lab Notes Because we used a chance mechanism to select our sample, each sample will differ. My data set (GerstmanB.sav), looks

### Offsets and Overdispersion

Offsets and Patrick Breheny April 11 Patrick Breheny BST 760: Advanced Regression 1/23 Poisson rates Offsets The meaning of λ often requires additional thought When we employ a Poisson model, what we are

### Sections 7.1 and 7.2. This chapter presents the beginning of inferential statistics. The two major applications of inferential statistics

Sections 7.1 and 7.2 This chapter presents the beginning of inferential statistics. The two major applications of inferential statistics Estimate a population parameter: proportion, mean Test some claim

### Math 1070 Exam 2B 22 March, 2013

Math 1070 Exam 2B 22 March, 2013 This exam will last 50 minutes and consists of 13 multiple choice and 6 free response problems. Write your answers in the space provided. All solutions must be sufficiently

### 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

### Sampling Distribution of a Sample Proportion

Sampling Distribution of a Sample Proportion From earlier material remember that if X is the count of successes in a sample of n trials of a binomial random variable then the proportion of success is given

### Genere e rischio cardiovascolare nel diabete. Giuseppe Seghieri

La salute e medicina di genere la ricerca sul campo focus su diabete e malattie croniche Genere e rischio cardiovascolare nel diabete. Giuseppe Seghieri Pistoia 7 giugno 2016, Ospedale San Jacopo _ Sala

### Sampling & Confidence Intervals

Sampling & Confidence Intervals Mark Lunt Arthritis Research UK Centre for Excellence in Epidemiology University of Manchester 18/10/2016 Principles of Sampling Often, it is not practical to measure every

### Structure of PhD thesis. Bernt Lindtjørn

Structure of PhD thesis Bernt Lindtjørn A PhD is a Research degree Thesis Synthesis A PhD thesis: A good example Variation in Malaria Transmission in Southern Ethiopia The impact of prevention strategies

### The calculations lead to the following values: d 2 = 46, n = 8, s d 2 = 4, s d = 2, SEof d = s d n s d n

EXAMPLE 1: Paired t-test and t-interval DBP Readings by Two Devices The diastolic blood pressures (DBP) of 8 patients were determined using two techniques: the standard method used by medical personnel

### SOLUTIONS: 4.1 Probability Distributions and 4.2 Binomial Distributions

SOLUTIONS: 4.1 Probability Distributions and 4.2 Binomial Distributions 1. The following table contains a probability distribution for a random variable X. a. Find the expected value (mean) of X. x 1 2

### Solutions to Homework 8 Statistics 302 Professor Larget

s to Homework 8 Statistics 302 Professor Larget Tetbook Eercises 6.12 Impact of the Population Proportion on SE Compute the standard error for sample proportions from a population with proportions p =

### 8.2 Confidence Intervals for One Population Mean When σ is Known

8.2 Confidence Intervals for One Population Mean When σ is Known Tom Lewis Fall Term 2009 8.2 Confidence Intervals for One Population Mean When σ isfall Known Term 2009 1 / 6 Outline 1 An example 2 Finding

### Randomized trials versus observational studies

Randomized trials versus observational studies The case of postmenopausal hormone therapy and heart disease Miguel Hernán Harvard School of Public Health www.hsph.harvard.edu/causal Joint work with James

### 5 Risk factors for the persistence of wheeze during childhood

5 Risk factors for the persistence of wheeze during childhood Asthma has a variable natural history, with onset and remission occurring at any age. Longitudinal studies suggest that the pattern of asthma

### This HW reviews the normal distribution, confidence intervals and the central limit theorem.

Homework 3 Solution This HW reviews the normal distribution, confidence intervals and the central limit theorem. (1) Suppose that X is a normally distributed random variable where X N(75, 3 2 ) (mean 75

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

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

### STATISTICS 8 CHAPTERS 1 TO 6, SAMPLE MULTIPLE CHOICE QUESTIONS

STATISTICS 8 CHAPTERS 1 TO 6, SAMPLE MULTIPLE CHOICE QUESTIONS Correct answers are in bold italics.. This scenario applies to Questions 1 and 2: A study was done to compare the lung capacity of coal miners

### AP Statistics Final Examination Multiple-Choice Questions Answers in Bold

AP Statistics Final Examination Multiple-Choice Questions Answers in Bold Name Date Period Answer Sheet: Multiple-Choice Questions 1. A B C D E 14. A B C D E 2. A B C D E 15. A B C D E 3. A B C D E 16.

### χ 2 = (O i E i ) 2 E i

Chapter 24 Two-Way Tables and the Chi-Square Test We look at two-way tables to determine association of paired qualitative data. We look at marginal distributions, conditional distributions and bar graphs.

### Stat 210 Exam Four. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Stat 210 Exam Four Read these directions carefully. As usual, you may pick any part of one problem to omit by writing OMIT in the answer blank (any one multiple choice or any one part of the other problems).

### 9.2 Examples. Example 1

9.2 Examples Example 1 A simple random sample of size n is drawn. The sample mean,, is found to be 19.2, and the sample standard deviation, s, is found to be 4.7. a) Construct a 95% confidence interval

### Statistical Inference

Statistical Inference Idea: Estimate parameters of the population distribution using data. How: Use the sampling distribution of sample statistics and methods based on what would happen if we used this

### Section 7.2 Confidence Intervals for Population Proportions

Section 7.2 Confidence Intervals for Population Proportions 2012 Pearson Education, Inc. All rights reserved. 1 of 83 Section 7.2 Objectives Find a point estimate for the population proportion Construct

### CHAPTER 8 ESTIMATION

CHAPTER 8 ESTIMATION CONFIDENCE INTERVALS FOR A POPULATION MEAN (SECTION 8.1 AND 8.2 OF UNDERSTANDABLE STATISTICS) The TI-83 Plus and TI-84 Plus fully support confidence intervals. To access the confidence

### Lecture #9 Tuesday, September 20, 2016 Textbook: Section 4.3, 5.1, 5.2, 5.3

STATISTICS 200 Lecture #9 Tuesday, September 20, 2016 Textbook: Section 4.3, 5.1, 5.2, 5.3 Objectives: Understand Simpson s paradox: What causes it, why it s surprising Contrast statistical significance

### Announcements. Unit 4: Inference for numerical variables Lecture 1: Bootstrap, paired, and two sample. Rent in Durham.

Announcements Announcements Unit 4: Inference for numerical variables Lecture 1: Bootstrap, paired, and two sample Statistics 101 Mine Çetinkaya-Rundel February 26, 2013 Extra credit due Thursday at the

### Chapter 8 Hypothesis Testing

Chapter 8 Hypothesis Testing Chapter problem: Does the MicroSort method of gender selection increase the likelihood that a baby will be girl? MicroSort: a gender-selection method developed by Genetics

### 6. Duality between confidence intervals and statistical tests

6. Duality between confidence intervals and statistical tests Suppose we carry out the following test at a significance level of 100α%. H 0 :µ = µ 0 H A :µ µ 0 Then we reject H 0 if and only if µ 0 does

### Hypothesis Testing. April 21, 2009

Hypothesis Testing April 21, 2009 Your Claim is Just a Hypothesis I ve never made a mistake. Once I thought I did, but I was wrong. Your Claim is Just a Hypothesis Confidence intervals quantify how sure

### Pooling and Meta-analysis. Tony O Hagan

Pooling and Meta-analysis Tony O Hagan Pooling Synthesising prior information from several experts 2 Multiple experts The case of multiple experts is important When elicitation is used to provide expert

### When Does it Make Sense to Perform a Meta-Analysis?

CHAPTER 40 When Does it Make Sense to Perform a Meta-Analysis? Introduction Are the studies similar enough to combine? Can I combine studies with different designs? How many studies are enough to carry

### MAT140: Applied Statistical Methods Summary of Calculating Confidence Intervals and Sample Sizes for Estimating Parameters

MAT140: Applied Statistical Methods Summary of Calculating Confidence Intervals and Sample Sizes for Estimating Parameters Inferences about a population parameter can be made using sample statistics for

### Hypothesis tests, confidence intervals, and bootstrapping

Hypothesis tests, confidence intervals, and bootstrapping Business Statistics 41000 Fall 2015 1 Topics 1. Hypothesis tests Testing a mean: H0 : µ = µ 0 Testing a proportion: H0 : p = p 0 Testing a difference

### Dealing with confounding in the analysis

Chapter 14 Dealing with confounding in the analysis In the previous chapter we discussed briefly how confounding could be dealt with at both the design stage of a study and during the analysis of the results.

### 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

### Confidence level. Most common choices are 90%, 95%, or 99%. (α = 10%), (α = 5%), (α = 1%)

Confidence Interval A confidence interval (or interval estimate) is a range (or an interval) of values used to estimate the true value of a population parameter. A confidence interval is sometimes abbreviated

PROBLEM SET 1 For the first three answer true or false and explain your answer. A picture is often helpful. 1. Suppose the significance level of a hypothesis test is α=0.05. If the p-value of the test

### 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

### 49. INFANT MORTALITY RATE. Infant mortality rate is defined as the death of an infant before his or her first birthday.

49. INFANT MORTALITY RATE Wing Tam (Alice) Jennifer Cheng Stat 157 course project More Risk in Everyday Life Risk Meter LIKELIHOOD of exposure to hazardous levels Low Medium High Consequences: Severity,

### Outline. 1 Confidence Intervals for Proportions. 2 Sample Sizes for Proportions. 3 Student s t-distribution. 4 Confidence Intervals without σ

Outline 1 Confidence Intervals for Proportions 2 Sample Sizes for Proportions 3 Student s t-distribution 4 Confidence Intervals without σ Outline 1 Confidence Intervals for Proportions 2 Sample Sizes for

### Chapter 14: 1-6, 9, 12; Chapter 15: 8 Solutions When is it appropriate to use the normal approximation to the binomial distribution?

Chapter 14: 1-6, 9, 1; Chapter 15: 8 Solutions 14-1 When is it appropriate to use the normal approximation to the binomial distribution? The usual recommendation is that the approximation is good if np

### Stat 20: Discussion at section

Stat 20: Discussion at section B. M. Bolstad, bolstad@stat.berkeley.edu Oct 20, 2003 Hypothesis tests To perform a hypothesis test we need to do the following things. (a.) State a null and alternative

### Estimating the population proportion p using the sample proportion ˆp

8.1 Sampling distributions What we ve already covered from 8.1 Distribution of the sample mean X What we re covering now in 8.1 Distribution of the sample proportion ˆp 1 Estimating the population proportion

### Chapter 6 Section 3 Homework A

Chapter 6 Section 3 Homework A 6.86 A role as a statistical consultant. You are the statistical expert for a graduate student planning her PhD research. After you carefully present the mechanics of significance

### Measures of disease frequency

Measures of disease frequency Madhukar Pai, MD, PhD McGill University, Montreal Email: madhukar.pai@mcgill.ca 1 Overview Big picture Measures of Disease frequency Measures of Association (i.e. Effect)

### in Singapore and provide valuable inputs for the the Ministry of Health conducts periodic, population-

5 Main Report H E A LT H SURVEY Introduction 1 Introduction N AT I O N A L Background The Epidemiology and Disease Control Division of in Singapore and provide valuable inputs for the the Ministry of

### Section 5 3 The Mean and Standard Deviation of a Binomial Distribution

Section 5 3 The Mean and Standard Deviation of a Binomial Distribution Previous sections required that you to find the Mean and Standard Deviation of a Binomial Distribution by using the values from a

### Lab 4 for Math 17: Probability and Simulation

Lab 4 for Math 17: Probability and Simulation 1 The Law of Total Probability and More The law of total probability gives us some additional options to find probabilities of events. For an event A, and

### 3. Confidence Interval (INTR)

31 3. Confidence Interval (INTR) A confidence interval is a range (interval) that includes the population mean value. A confidence interval that is too broad makes it difficult to get an idea of where

### Confidence Interval: pˆ = E = Indicated decision: < p <

Hypothesis (Significance) Tests About a Proportion Example 1 The standard treatment for a disease works in 0.675 of all patients. A new treatment is proposed. Is it better? (The scientists who created