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144 CHAPTER 5 SOME IMPORTANT SAMPLING DISTRIBUTIONS limit theorem and transform the resulting approximately normal sampling distribution p of x (which has a mean of 120 and a standard deviation of 15= ffiffiffiffiffi 50 ¼ 2:1213) to the standard normal. The probability we seek is 115 120 125 120 Pð115 x 125Þ ¼ P z 2:12 2:12 ¼ Pð 2:36 z 2:36Þ ¼ :9909 :0091 ¼ :9818 & EXERCISES 5.3.1 The National Health and Nutrition Examination Survey of 1988–1994 (NHANES III, A-1) estimated the mean serum cholesterol level for U.S. females aged 20–74 years to be 204 mg/dl. The estimate of the standard deviation was approximately 44. Using these estimates as the mean m and standard deviation s for the U.S. population, consider the sampling distribution of the sample mean based on samples of size 50 drawn from women in this age group. What is the mean of the sampling distribution? The standard error? 5.3.2 The study cited in Exercise 5.3.1 reported an estimated mean serum cholesterol level of 183 for women aged 20–29 years. The estimated standard deviation was approximately 37. Use these estimates as the mean m and standard deviation s for the U.S. population. If a simple random sample of size 60 is drawn from this population, find the probability that the sample mean serum cholesterol level will be: (a) Between 170 and 195 (b) Below 175 (c) Greater than 190 5.3.3 If the uric acid values in normal adult males are approximately normally distributed with a mean and standard deviation of 5.7 and 1 mg percent, respectively, find the probability that a sample of size 9 will yield a mean: (a) Greater than 6 (b) Between 5 and 6 (c) Less than 5.2 5.3.4 Wright et al. [A-2] used the 1999–2000 National Health and Nutrition Examination Survey (NHANES) to estimate dietary intake of 10 key nutrients. One of those nutrients was calcium (mg). They found in all adults 60 years or older a mean daily calcium intake of 721 mg with a standard deviation of 454. Using these values for the mean and standard deviation for the U.S. population, find the probability that a random sample of size 50 will have a mean: (a) Greater than 800 mg (b) Less than 700 mg (c) Between 700 and 850 mg 5.3.5 In the study cited in Exercise 5.3.4, researchers found the mean sodium intake in men and women 60 years or older to be 2940 mg with a standard deviation of 1476 mg. Use these values for the mean and standard deviation of the U.S. population and find the probability that a random sample of 75 people from the population will have a mean: (a) Less than 2450 mg (b) Over 3100 mg (c) Between 2500 and 3300 mg (d) Between 2500 and 2900 mg
5.4 DISTRIBUTION OF THE DIFFERENCE BETWEEN TWO SAMPLE MEANS 145 5.3.6 Given a normally distributed population with a mean of 100 and a standard deviation of 20, find the following probabilities based on a sample of size 16: (a) Pðx 100Þ (b) Pðx 110Þ (c) Pð96 x 108Þ 5.3.7 Given m ¼ 50; s ¼ 16, and n ¼ 64, find: (a) Pð45 x 55Þ (b) Pðx > 53Þ (c) Pðx < 47Þ (d) Pð49 x 56Þ 5.3.8 Suppose a population consists of the following values: 1, 3, 5, 7, 9. Construct the sampling distribution of x based on samples of size 2 selected without replacement. Find the mean and variance of the sampling distribution. 5.3.9 Use the data of Example 5.3.1 to construct the sampling distribution of x based on samples of size 3 selected without replacement. Find the mean and variance of the sampling distribution. 5.3.10 Use the data cited in Exercise 5.3.1. Imagine we take samples of size 5, 25, 50, 100, and 500 from the women in this age group. (a) Calculate the standard error for each of these sampling scenarios. (b) Discuss how sample size affects the standard error estimates calculated in part (a) and the potential implications this may have in statistical practice. 5.4 DISTRIBUTION OF THE DIFFERENCE BETWEEN TWO SAMPLE MEANS Frequently the interest in an investigation is focused on two populations. Specifically, an investigator may wish to know something about the difference between two population means. In one investigation, for example, a researcher may wish to know if it is reasonable to conclude that two population means are different. In another situation, the researcher may desire knowledge about the magnitude of the difference between two population means. A medical research team, for example, may want to know whether or not the mean serum cholesterol level is higher in a population of sedentary office workers than in a population of laborers. If the researchers are able to conclude that the population means are different, they may wish to know by how much they differ. A knowledge of the sampling distribution of the difference between two means is useful in investigations of this type. Sampling from Normally Distributed Populations The following example illustrates the construction of and the characteristics of the sampling distribution of the difference between sample means when sampling is from two normally distributed populations. EXAMPLE 5.4.1 Suppose we have two populations of individuals—one population (population 1) has experienced some condition thought to be associated with mental retardation, and the other population (population 2) has not experienced the condition. The distribution of
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TENTH EDITION BIOSTATISTICS A Found
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VP & EXECUTIVE PUBLISHER: ACQUISITI
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PREFACE This 10th edition of Biosta
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PREFACE ix SUPPLEMENTS Instructor
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BRIEF CONTENTS 1 INTRODUCTION TO BI
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xiv CONTENTS 6.3 The t Distribution
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CHAPTER1 INTRODUCTION TO BIOSTATIST
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1.2 SOME BASIC CONCEPTS 3 Sources o
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1.3 MEASUREMENT AND MEASUREMENT SCA
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1.4 SAMPLING AND STATISTICAL INFERE
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1.5 THE SCIENTIFIC METHOD AND THE D
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1.6 COMPUTERS AND BIOSTATISTICAL AN
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REVIEW QUESTIONS AND EXERCISES 17 a
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CHAPTER2 DESCRIPTIVE STATISTICS CHA
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2.2 THE ORDERED ARRAY 21 TABLE 2.2.
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2.3 GROUPED DATA: THE FREQUENCY DIS
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EXERCISES 31 3 ¼ an abundance of s
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EXERCISES 33 25.21 30.49 27.38 36.4
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EXERCISES 35 2.3.7 In a study of ph
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EXERCISES 37 0.6870 0.6900 0.6910 0
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2.4 DESCRIPTIVE STATISTICS: MEASURE
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EXERCISES 53 2.5.1 Porcellini et al
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SUMMARY OF FORMULAS FOR CHAPTER 2 5
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REVIEW QUESTIONS AND EXERCISES 57 R
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REVIEW QUESTIONS AND EXERCISES 59 1
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REFERENCES 63 DRINK TOUNCES TGRAMS
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CHAPTER3 SOME BASIC PROBABILITY CON
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3.2 TWO VIEWS OF PROBABILITY: OBJEC
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3.4 CALCULATING THE PROBABILITY OF
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EXERCISES 77 (d) If we pick a subje
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3.5 BAYES’ THEOREM, SCREENING TES
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3.5 BAYES’ THEOREM, SCREENING TES
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EXERCISES 83 EXERCISES 3.5.1 A medi
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REVIEW QUESTIONS AND EXERCISES 87 (
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REVIEW QUESTIONS AND EXERCISES 89 i
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REFERENCES 91 Applications Referenc
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Page 151 and 152: REFERENCES 133 REFERENCES Methodolo
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Page 179 and 180: CHAPTER6 ESTIMATION CHAPTER OVERVIE
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6.9 CONFIDENCE INTERVAL FOR THE VAR
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EXERCISES 197 x 2 1 ða=2Þ ¼ 14:4
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6.10 CONFIDENCE INTERVAL FOR THE RA
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6.10 CONFIDENCE INTERVAL FOR THE RA
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REVIEW QUESTIONS AND EXERCISES 205
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REFERENCES 211 3. W. V. BEHRENS,
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REFERENCES 213 A-30. ELENI KOUSTA,
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7.1 INTRODUCTION 215 7.1 INTRODUCTI
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7.1 INTRODUCTION 217 question: Can
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7.1 INTRODUCTION 219 DEFINITION The
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7.1 INTRODUCTION 221 Evaluate data
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7.2 HYPOTHESIS TESTING: A SINGLE PO
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EXERCISES 233 Dialog box: Session c
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EXERCISES 235 7.2.10 Following a we
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7.3 HYPOTHESIS TESTING: THE DIFFERE
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EXAMPLE 7.3.2 The purpose of a stud
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EXERCISES 245 The SAS System The TT
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EXERCISES 247 Primary Hypertensive
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7.4 PAIRED COMPARISONS 249 7.3.10 R
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7.4 PAIRED COMPARISONS 251 where d
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7.4 PAIRED COMPARISONS 253 a = .05
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EXERCISES 255 7.4.1 Ellen Davis Jon
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EXERCISES 263 MINITAB Output Test a
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7.8 HYPOTHESIS TESTING: THE RATIO O
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7.8 HYPOTHESIS TESTING: THE RATIO O
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EXERCISES 271 EXERCISES In the foll
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7.9 THE TYPE II ERROR AND THE POWER
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7.9 THE TYPE II ERROR AND THE POWER
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7.10 DETERMINING SAMPLE SIZE TO CON
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EXERCISES 279 We set the right-hand
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REFERENCES 301 A-17. JOHN S. MORLEY
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REFERENCES 303 A-56. LUIGI BENINI,
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8.1 INTRODUCTION 305 8.1 INTRODUCTI
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8.1 INTRODUCTION 307 who received d
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8.2 THE COMPLETELY RANDOMIZED DESIG
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Dependent Variable: Selenium Tukey
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EXERCISES 329 Elbow Angle (Degrees)
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EXERCISES 331 Age Groups (Years) Ag
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EXERCISES 333 Group 1 Group 2 Group
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Objective The objective in using th
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8.3 THE RANDOMIZED COMPLETE BLOCK D
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EXERCISES 343 The SAS System Analys
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EXERCISES 345 group were randomly a
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8.4 THE REPEATED MEASURES DESIGN 34
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EXERCISES 357 Is there sufficient e
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8.5 THE FACTORIAL EXPERIMENT 359 In
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8.5 THE FACTORIAL EXPERIMENT 361 In
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8.5 THE FACTORIAL EXPERIMENT 363 Be
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8.5 THE FACTORIAL EXPERIMENT 365 TA
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8.5 THE FACTORIAL EXPERIMENT 367 Ro
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EXERCISES 369 The SAS System Analys
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EXERCISES 371 Physical Psychiatric
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8.6 SUMMARY 373 Percent Change in C
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REFERENCES 409 Applications Referen
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REFERENCES 411 Postmenopausal Women
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CHAPTER9 SIMPLE LINEAR REGRESSION A
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9.2 THE REGRESSION MODEL 415 some e
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9.3 THE SAMPLE REGRESSION EQUATION
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EXERCISES EXERCISES 423 The Least-S
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EXERCISES 425 CoaguChek Hospital Co
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9.4 EVALUATING THE REGRESSION EQUAT
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9.5 USING THE REGRESSION EQUATION I
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9.5 USING THE REGRESSION EQUATION 4
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9.6 THE CORRELATION MODEL 445 9.6 T
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9.7 THE CORRELATION COEFFICIENT 447
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EXERCISES 455 is employed. We first
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EXERCISES 457 9.7.3 In the study by
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9.8 SOME PRECAUTIONS 459 X Y X Y 5.
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9.9 SUMMARY 461 variance, which tes
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9.7.3 t statistic for correlation c
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REFERENCES 487 A-4. ROBERT B. PARKE
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CHAPTER10 MULTIPLE REGRESSION AND C
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Assumptions follows. 10.2 THE MULTI
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10.3 OBTAINING THE MULTIPLE REGRESS
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10.3 OBTAINING THE MULTIPLE REGRESS
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EXERCISES 497 EXERCISES Obtain the
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EXERCISES 499 10.3.3 In a study of
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10.4 EVALUATING THE MULTIPLE REGRES
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10.5 USING THE MULTIPLE REGRESSION
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EXERCISES 509 and has an education
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10.6 THE MULTIPLE CORRELATION MODEL
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This equation may be used for estim
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EXERCISES 521 HIV DNA Blood (Y) HIV
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SUMMARY OF FORMULAS FOR CHAPTER 10
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10.6.7 t statistic for testing hypo
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REFERENCES 537 4. Refer to the data
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CHAPTER11 REGRESSION ANALYSIS: SOME
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11.1 INTRODUCTION 541 TABLE 11.1.1
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11.2 QUALITATIVE INDEPENDENT VARIAB
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EXERCISES 557 11.2.1 For subjects u
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EXERCISES 559 11.2.4 Refer to Exerc
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11.3 VARIABLE SELECTION PROCEDURES
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11.3 VARIABLE SELECTION PROCEDURES
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EXERCISES 565 CGAGE CGINCOME CGDUR
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EXERCISES 567 11.3.2 Machiel Naeije
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11.4 LOGISTIC REGRESSION 569 REACTI
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11.4 LOGISTIC REGRESSION 571 betwee
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11.4 LOGISTIC REGRESSION 573 The LO
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11.4 LOGISTIC REGRESSION 575 Standa
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11.4 LOGISTIC REGRESSION 577 Parame
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11.4 LOGISTIC REGRESSION 579 Model
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EXERCISES EXERCISES 581 Further Rea
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REFERENCES 597 KNOW ¼ Knowledge. S
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REFERENCES 599 A-26. EITHNE MULLOYa
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12.1 INTRODUCTION 12.2 THE MATHEMAT
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12.2 THE MATHEMATICAL PROPERTIES OF
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12.3 TESTS OF GOODNESS-OF-FIT 605 W
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12.3 TESTS OF GOODNESS-OF-FIT 607 x
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12.3 TESTS OF GOODNESS-OF-FIT 609 9
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that the first expected frequency i
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12.3 TESTS OF GOODNESS-OF-FIT 613 T
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12.3 TESTS OF GOODNESS-OF-FIT 615 V
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EXERCISES 617 EXERCISES 12.3.1 The
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12.4 TESTS OF INDEPENDENCE 619 12.3
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Observed Versus Expected Frequencie
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12.4 TESTS OF INDEPENDENCE 623 Comp
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12.4 TESTS OF INDEPENDENCE 625 Note
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12.4 TESTS OF INDEPENDENCE 627 9. C
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EXERCISES 629 Performed Baseline Te
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12.5 TESTS OF HOMOGENEITY 631 TABLE
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12.5 TESTS OF HOMOGENEITY 633 8. St
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EXERCISES 635 12.5.2 Coughlin et al
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Hypotheses alternatives. 12.6 THE F
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12.6 THE FISHER EXACT TEST 639 TABL
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12.7 RELATIVE RISK, ODDS RATIO, AND
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EXERCISES 653 Smoking_status * Obse
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12.8 SUMMARY 655 collected data on
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REFERENCES 667 12. R. LATSCHA, “T
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REFERENCES 669 A-35. CRAIG R. COHEN
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13.1 INTRODUCTION 671 2. be able to
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13.3 THE SIGN TEST 673 13.3 THE SIG
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13.3 THE SIGN TEST 675 TABLE 13.3.2
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13.3 THE SIGN TEST 677 EXAMPLE 13.3
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13.3 THE SIGN TEST 679 one sample i
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13.4 THE WILCOXON SIGNED-RANK TEST
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13.4 THE WILCOXON SIGNED-RANK TEST
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13.5 THE MEDIAN TEST 687 TABLE 13.5
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EXAMPLE 13.6.1 A researcher designe
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13.6 THE MANN-WHITNEY TEST 693 to t
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13.6 THE MANN-WHITNEY TEST 695 Dial
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EXERCISES 697 deficit in Sprague-Da
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Assumptions the following: 1. The s
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13.7 THE KOLMOGOROV-SMIRNOV GOODNES
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EXERCISES 703 1.0 .9 Cumulative rel
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13.8 THE KRUSKAL-WALLIS ONE-WAY ANA
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13.8 THE KRUSKAL-WALLIS ONE-WAY ANA
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EXERCISES 709 Data: C1: 12.22 28.44
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EXERCISES 711 Improvement (Control)
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13.9 THE FRIEDMAN TWO-WAY ANALYSIS
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13.9 THE FRIEDMAN TWO-WAY ANALYSIS
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EXERCISES 717 Subject Area Student
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13.10 THE SPEARMAN RANK CORRELATION
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EXERCISES 725 Rank by Rank by Area
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13.11 NONPARAMETRIC REGRESSION ANAL
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13.11 NONPARAMETRIC REGRESSION ANAL
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REFERENCES 747 cardiac operations.
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REFERENCES 749 A-14. WENDY GANTT an
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14.2 TIME-TO-EVENT DATA AND CENSORI
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14.3 THE KAPLAN-MEIER PROCEDURE 757
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14.3 THE KAPLAN-MEIER PROCEDURE 759
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EXERCISES 761 1.0 .8 73% Low-grade
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14.4 COMPARING SURVIVAL CURVES 763
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14.4 COMPARING SURVIVAL CURVES 765
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EXERCISES 767 EXERCISES 14.4.1 If a
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14.5 COX REGRESSION: THE PROPORTION
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14.5 COX REGRESSION: THE PROPORTION
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REFERENCES 777 REFERENCES Methodolo
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A-2 APPENDIX STATISTICAL TABLES
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ANSWERS TO ODD-NUMBERED EXERCISES C
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ANSWERS TO ODD-NUMBERED EXERCISES A
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I-2 INDEX Confidence coefficient, 1
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I-4 INDEX Median test, 686-689 MINI
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I-6 INDEX SAS: and chi-square analy
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Biostatistics

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