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where with d.f. = 1 Hypothesis Test with . . 1 d d d d dE d E s Et n n d t df n s n α µ µ −+ =− − = = − Two Sample Variances 22 2 2 12 2 22 1 11 2 2 2 2 2 1 2 2 2 12 2 12 Confidence Interval for and 11 Hypothesis Test Statistic: where numerator . . 1 and denominator . . 1 right left ss ss FF s F ss s df n df n σ σ σ σ • << •
INTRODUCTION TO STATISTICAL ANALYSIS. LEARNING OBJECTIVES: After studying this chapter, a student should understand: notation used in statistics; how to represent variables in a mathematical form for statistical purposes; how to construct frequency distributions, histograms, and bar graphs;
An estimator ^ n (depending on n iid samples) of is said to be consistent if it converges (in probability) to . That is, for any " > 0, lim P j^ n j > " = 0 n!1. Basically, as n ! 1, ^ n in the limit will be extremely close to . As usual, we'll do some examples to see how to show this. Example(s)
1 Introduction 1 1.1 Simple Linear Regression Model 1 1.2 Multiple Linear Regression Model 2 1.3 Analysis-of-Variance Models 3 2 Matrix Algebra 5 2.1 Matrix and Vector Notation 5 2.1.1 Matrices, Vectors, and Scalars 5 2.1.2 Matrix Equality 6 2.1.3 Transpose 7 2.1.4 Matrices of Special Form 7 2.2 Operations 9 2.2.1 Sum of Two Matrices or Two ...
1 ••• Master List of Formulas Chapter 1 IntroduCtIon and desCrIptIve statIstICs NONE. Chapter 2 FrequenCy dIstrIbutIons In tables and Graphs Σx (Frequency) Σx n (Relative frequency) Σx n × 100 (Relative percent) Chapter 3 summarIzInG data: Center tendenCy µ= Σx N (Population mean) M = Σx n (Sample mean) M Mn w n = Σ × Σ (Weighted sample mean) Chapter 4 summarIzInG data: varIabIlIty
9.5 Additional Information and Full Hypothesis Test Examples . . . . . . . . . . . . . . . . . . 482 9.6 Hypothesis Testing of a Single Mean and Single Proportion .
Probability Density Function (PDF) A PDF2 is a normalized, distribution which tells you the probability of a finding your variable in some interval Random variable x3 PDF p(x) then Prob(a <x <b) = Z b a p(x)dx (1) The probability interpretation only makes sense if you must find your variable somewhere! 1 = Z 1 0 p(x)dx (2)
