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10 Contents
Conditional Distributions 73
Independence 77
Covariance and Correlation 77
The Mean and Variance of Sums of Random Variables 78
2.4 The Normal, Chi-Squared, Student t, and F Distributions 82
The Normal Distribution 82
The Chi-Squared Distribution 87
The Student t Distribution 87
The F Distribution 88
2.5 Random Sampling and the Distribution of the Sample Average 89
Random Sampling 89
The Sampling Distribution of the Sample Average 90
2.6 Large-Sample Approximations to Sampling Distributions 93
The Law of Large Numbers and Consistency 94
The Central Limit Theorem 96
Appendix 2.1 Derivation of Results in Key Concept 2.3 109
Chapter 3 Review of Statistics 111
3.1 Estimation of the Population Mean 112
Estimators and Their Properties 112
Properties of Y 114
The Importance of Random Sampling 116
3.2 Hypothesis Tests Concerning the Population Mean 117
Null and Alternative Hypotheses 117 120
The p-Value 118
Calculating the p-Value When sY Is Known 119
The Sample Variance, Sample Standard Deviation, and Standard Error
Calculating the p-Value When sY Is Unknown 122
The t-Statistic 122
Hypothesis Testing with a Prespecified Significance Level 123
One-Sided Alternatives 125
3.3 Confidence Intervals for the Population Mean 126
3.4 Comparing Means from Different Populations 128
Hypothesis Tests for the Difference Between Two Means 128
Confidence Intervals for the Difference Between Two Population Means 130
