1 Basic Statistical Concepts 1

Contents

• Basic Statistical Concepts1

1.2 Populations and Samples........................... 1 1.3 Some Sampling Concepts........................... 2 1.4 Random Variables and Statistical Populations............... 3 1.5 Basic Graphics for Data Visualization.................... 4 1.6 Proportions,Averages,andVariances.................... 20 1.7 Medians,Percentiles,andBoxplots ..................... 23 1.8 Comparative Studies............................. 24

• Introduction to Probability35

2.2 Sample Spaces, Events, and Set Operations................. 35 2.3 ExperimentswithEquallyLikelyOutcomes ................ 39 2.4 Axioms and Properties of Probabilities................... 44 2.5 Conditional Probability............................ 47 2.6 IndependentEvents.............................. 51

• Random Variables and Their Distributions53

3.2 Describing a Probability Distribution.................... 53 3.3 Parameters of Probability Distributions................... 59 3.4 ModelsforDiscreteRandomVariables ................... 63 3.5 ModelsforContinuousRandomVariables ................. 68

• Jointly Distributed Random Variables77

4.2 Describing Joint Probability Distributions................. 77 4.3 Conditional Distributions . . ......................... 79 4.4 MeanValueofFunctionsofRandomVariables............... 87 4.5 QuantifyingDependence ........................... 93 4.6 Models for Joint Distributions........................ 97

• Some Approximation Results103

5.2 TheLLNandtheConsistencyofAverages................. 103 5.3 Convolutions ................................. 104 5.4 The Central Limit Theorem......................... 106 Probability & Statistics wi th R for Engineers and Scientists, 1e Michael Akritas (Solutions Ma nual All Chapters, 100% Original Verified, A+ Grade) 1 / 4

CONTENTS

• Fitting Models to Data 111

6.2 SomeEstimationConcepts.......................... 111 6.3 MethodsforFittingModelstoData..................... 113

6.4 ComparingEstimators:TheMSECriterion ................ 119

• Confidence and Prediction Intervals 121

7.3 Type of Confidence Intervals......................... 121 7.4 The Issue of Precision............................ 129 7.5 PredictionIntervals.............................. 130

• Testing of Hypotheses 133

8.2 SettingUpaTestProcedure......................... 133 8.3 TypesofTests................................. 136 8.4 PrecisioninHypothesisTesting ....................... 144

• Comparing Two Populations 147

9.2 Two-Sample Tests and CIs for Means.................... 147 9.3 TheRank-SumTestProcedure ....................... 155 9.4 ComparingTwoVariances.......................... 158 9.5 PairedData.................................. 159 10 Comparingk>2Populations 163 10.2 Types ofk-Sample Tests........................... 163 10.3 Simultaneous CIs and Multiple Comparisons................ 173 10.4RandomizedBlockDesigns.......................... 181 11 Multifactor Experiments 187 11.2Two-FactorDesigns.............................. 187 11.3Three-FactorDesigns............................. 194

11.4 2

r FactorialExperiments........................... 199 12 Polynomial and Multiple Regression 209 12.2 The Multiple Linear Regression Model................... 209 12.3Estimating,Testing,andPrediction..................... 212 12.4 Additional Topics............................... 221 13 Statistical Process Control 237 13.2 The ¯ XChart ................................. 237 13.3 TheSandRCharts ............................. 242 13.4 ThepandcCharts.............................. 246 13.5CUSUMandEWMACharts......................... 249 Copyright©2016 Pearson Education, Inc. 2 / 4

1 Chapter 1 Basic Statistical Concepts 1.2 Populations and Samples

• (a) The population consists of the customers who bought a car during the previous

year.(b) The population is not hypothetical.

• (a) There are three populations, one for each variety of corn. Each variety of corn

that has been and will be planted on all kinds of plots make up the population.(b) The characteristic of interest is the yield of each variety of corn at the time of harvest.(c) There are three samples, one for each variety of corn. Each variety of corn that was planted on the 10 randomly selected plots make up the sample.

• (a) There are two populations, one for each shift. The cars that have been and

will be produced on each shift make up the population.(b) The populations are hypothetical.(c) The characteristic of interest is the number of nonconformances per car.

• (a) The population consists of the all domestic flights, past or future.

(b) The sample consists of the 175 domestic flights.(c) The characteristic of interest is the air quality, quantified by the degree of staleness.

• (a) There are two populations, one for each teaching method.

(b) The population consists of all students who took or will take a statistics course for engineering using one of each teaching methods.(c) The populations are hypothetical.(d) The samples consist of the students whose scores will be recorded at the end of the semester.Copyright©2016 Pearson Education, Inc. 3 / 4

• Chapter 1 Basic Statistical Concepts

1.3 Some Sampling Concepts

• The second choice provides a closer approximation to simple random sample.
• (a) It is not a simple random sample.

(b) In (a), each member of the population does not have equal chance to be selected, thus it is not a simple random sample. Instead, the method described in (a) is a stratified sampling.

• (a) The population includes all the drivers in the university town.

(b) The student’s classmates do not constitute a simple random sample.(c) It is a convenient sample.(d) Young college students are not experienced drivers, thus they tend to use seat belts less. Consequently, the sample in this problem will underestimate the proportion.

• We identify each person with a number from 1 to 70. Then we write each number

from 1 to 70 on separate, identical slips of paper, put all 70 slips of paper in a box, and mix them thoroughly. Finally, we select 15 slips from the box, one at a time, without replacement. The 15 selected numbers specify the desired sample of size n= 15 from the 70 iPhones. The R command is y = sample(seq(1,70), size=15) A sample set is 52 8 14 48 62 6 70 35 18 20 3 41 50 27 40.

• We identify each pipe with a number from 1 to 90. Then we write each number

from 1 to 90 on separate, identical slips of paper, put all 90 slips of paper in a box, and mix them thoroughly. Finally, we select 5 slips from the box, one at a time, without replacement. The 5 selected numbers specify the desired sample of size n= 5 from the 90 drain pipes. The R command is y = sample(seq(1,90), size=5), A sample set is 7 38 65 71 57.

• (a) We identify each client with a number from 1 to 1000. Then we write each

number from 1 to 1000 on separate, identical slips of paper, put all 1000 slips of paper in a box, and mix them thoroughly. Finally, we select 100 slips from the box, one at a time, without replacement. The 100 selected numbers specify the desired sample of sizen= 100 from the 1000 clients.Copyright©2016 Pearson Education, Inc.

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