Statistics the Easy Way

by Downing, Douglas; Clark, Jeff

• ISBN13: 9780812093926
• ISBN10: 0812093925
• Edition: 3rd
• Format: Paperback
• Copyright: 1997-03-01
• Publisher: Barrons Test Prep

Summary

These books are ideal students self-help supplements. They offer valuable overviews of course work and extra help with difficult subject areas. This volume explains probability, random variables, distributions, laws of large numbers and the central limit theorem, polls and sampling, linear regression, and much more. Hundreds of exercises with selected answers, plus programs in BASIC.

Author Biography

Douglas Downing teaches economics at Seattle Pacific University. He is the author of several books in the Easy Way series: Algebra, Trigonometry, Calculus, Computer Programming in BASIC, and Computer Programing in Pascal (with Mark Yoshimi), along with Dictionary of Mathematics Terms, and Dictionary of Computer and Internet Terms (with Michael and Melody Covington). He holds the Ph.D. degree in economics from Yale University. Jeffrey Clark teaches mathematics at Elon College. He is the author of Business Statistics and Quantitative Methods (both with Douglas Downing for the Barron's Business Review series). He holds the Ph.D. degree in mathematics from Yale University.

Table of Contents

Introduction	viii
Cast of Greek Characters (and Other Symbols)	x
Introduction To Statistics	1	(4)
Introduction To Probability	5	(4)
Exercises	9	(2)
Introduction To Hypothesis Testing	11	(5)
Exercises	15	(1)
Descriptive Statistics	16	(9)
Mean and Median	16	(1)
Variance	17	(3)
Frequency Histograms	20	(2)
Exercises	22	(3)
Definition Of Probability	25	(18)
Interpretations of Probability	25	(1)
Random Events	26	(1)
Probability Spaces	26	(2)
Probability of an Event	28	(3)
Probability of a Union (A or B)	31	(1)
Probability of an Intersection (A and B)	32	(3)
Axioms of Probability	35	(1)
Continuous Probability Spaces	36	(1)
Unions of Three or More Events	37	(3)
Exercises	40	(3)
Calculating Probabilities By Counting Outcomes	43	(20)
Multiplication Principle	43	(1)
Sampling with Replacement	44	(2)
Sampling Without Replacement	46	(1)
Permutations	47	(1)
Combinations	48	(9)
Multinomial Formula	57	(1)
Exercises	58	(5)
Conditional Probability	63	(10)
Calculating Conditional Probabilities	64	(2)
Independent Events	66	(2)
Bayes's Rule	68	(3)
Exercises	71	(2)
Discrete Random Variables	73	(17)
Probability Functions	74	(4)
Expectation	78	(3)
Variance	81	(3)
Bernoulli Trials	84	(1)
Choosing One Item from a List of Items	85	(2)
Exercises	87	(3)
The Binomial Distribution	90	(10)
Exercises	98	(2)
Other Discrete Distributions	100	(11)
The Poisson Distribution	100	(3)
The Geometric and Negative Binomial Distributions	103	(2)
The Hypergeometric Distribution	105	(3)
Exercises	108	(3)
Continuous Random Variables	111	(10)
Continuous Cumulative Distribution Functions	112	(1)
Continuous Probability Density Functions	113	(4)
Expectation and Variance	117	(2)
Exercises	119	(2)
The Normal Distribution	121	(15)
The Normal Density Function	121	(3)
The Standard Normal Density Function	124	(5)
Exercises	129	(3)
Moment Generating Functions	132	(3)
Exercises	135	(1)
Other Continuous Distributions	136	(9)
The Chi-square Distribution	136	(3)
The t Distribution	139	(1)
The Exponential Distribution	140	(3)
Exercises	143	(2)
Distributions With Two Random Variables	145	(14)
Joint Density Functions	145	(2)
Marginal Density Functions for Individual Random Variables	147	(1)
Conditional Density Functions	148	(1)
Independent Random Variables	148	(1)
Covariance and Correlation	149	(4)
Variance of a Sum	153	(1)
The Multinomial Distribution	154	(1)
Exercises	155	(4)
Law Of Large Numbers And Central Limit Theorem	159	(16)
Markov's Inequality	159	(1)
Chebyshev's Inequality	160	(2)
Law of Large Numbers	162	(1)
Central Limit Theorem	163	(6)
The Proof of the Central Limit Theorem	169	(4)
Strong Low of Large Numbers	173	(1)
Exercises	173	(2)
Statistical Estimation	175	(7)
Estimating the Mean	176	(1)
Maximum Likelihood Estimators	177	(1)
Consistent Estimators	178	(1)
Unbiased Estimators	178	(2)
Derivation of the Maximum Likelihood Estimator for the Mean	180	(1)
Exercises	181	(1)
Accuracy Of Estimates	182	(12)
Confidence Intervals	183	(2)
Calculating Confidence Intervals by Using the t Distribution	185	(5)
The Distribution of the Sample Variance	190	(2)
Exercises	192	(2)
Hypothesis Testing	194	(32)
Test Statistics	194	(3)
Testing the Value of the Mean	197	(3)
One-tailed Tests	200	(1)
Testing Hypotheses About the Probability of Success	201	(1)
Testing for the Difference Between Two Means	202	(3)
Paired Samples	205	(1)
Testing for the Difference Between Two Proportions	206	(2)
The Chi-square Test	208	(4)
Goodness-of-fit Tests	212	(1)
Analysis of Variance	213	(4)
Sum of Squares	217	(5)
Derivation of the F Statistic	222	(1)
Exercises	223	(3)
Sampling And Experimental Design	226	(14)
Opinion Polls	226	(8)
Confidence Interval for Proportion	234	(2)
Experimental Design	236	(2)
Exercises	238	(2)
Nonparametric Methods	240	(12)
Sign Test	240	(1)
Friedman Fr Test	241	(2)
Wilcoxon Rank Sum Test	243	(1)
Kruskal-Wallis H Test	244	(1)
Wilcoxon Signed Rank Test	245	(2)
Exercises	247	(5)
Regression With One Independent Variable	252	(29)
The Regression Line	255	(3)
Calculating a Regression Line	258	(3)
Accuracy of the Regression Line	261	(3)
Statistical Analysis of Regressions	264	(5)
Predicting Values of the Dependent Variable	269	(4)
Analysis of Residuals	273	(3)
Transformations with Logarithms	276	(3)
Exercises	279	(2)
Multiple Regression	281	(16)
Several Independent Variables	281	(3)
Multiple Regression Output	284	(3)
Further Analysis of Regression Models	287	(2)
Multiple Regression Calculation	289	(5)
Exercises	294	(3)
Fallacies And Traps	297	(12)
Appendix 1 Answers To Selected Exercises	309	(65)
Appendix 2 Using Calculators And Computers	374	(5)
Statistical Calculations on a Calculator	374	(1)
Statistical Calculations Using a Computer Software Package	375	(1)
Statistical Functions in the Microsoft Excel Spreadsheet	376	(3)
Appendix 3 Statistical Tables	379	(10)
One-tailed Standard Normal (Z) Random Variable Table	380	(2)
Two-tailed Standard Normal (Z) Random Variable Table	382	(1)
Chi Square Table	383	(1)
One-tailed t Distribution Table	384	(1)
Two-tailed t Distribution Table	385	(1)
F Distribution Table	386	(3)
Index	389