Introduction to Statistical Inference

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Buddy Collins
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1 Itroductio to Statistical Iferece Fial Review CH1: Picturig Distributios With Graphs 1. Types of Variable -Categorical -Quatitative 2. Represetatios of Distributios (a) Categorical -Pie Chart -Bar Graph (b) Quatitative -Ste/Leaf plot -Histogra CH2: Nuerical Suaries of Distributios 1. Mea 2. Media 3. Quartiles 4. Box-Plot 5. Outliers 6. Variace/Stadard Deviatio CH3: Noral Distributios 1. Defiitio of a Desity Rule 3. Fidig Noral Probabilities/ Proportios (Stadardizig) 4. Fidig Noral Percetiles (z-scores) -Ex: Fid c so that P (N(3, 5) c) =.12 CH4: Scatterplots ad Correlatio 1. How to ake a scatter plot 2. Associatio i Data (Liear, Positive, Negative) 3. Correlatio Coefficiet CH5: Regressio 1. Least Squares Regressio Lie ŷ(x) = (r s y s x )x + (ȳ x(r s y s x )) 2. Purpose of Least Squares Regressio Lie

2 3. Predictio usig Least Squares Regressio lie CH8/9: Producig Data Saples 1. Defiitio: Siple Rado Saple 2. Saplig Issues Exaples: Bias Geerated By Volutary Respose, etc 3. Def: Double Blid Experiets 4. Lurkig Variables CH10: Itroductio to Probability 1. Probability Model (a) Saple Space-S (b) Set of Evets- S (c) Assiget of Probabilities- P 2. Rules of Probability: If A ad B are disjoit evets (do t share ay outcoes): (a) 0 P (A) 1 (b) P (S) = 1 (c) P (A happes OR B happes) = P (A) + P (B) (d) If all outcoes i the saple space are equally likely the P (A) = CH11: Saplig Distributios 1. Defiitio: Paraeter/Statistic Nuber of outcoes i A Total Nuber of outcoes 2. If X 1,..., X N(µ, σ) are oral observatios with ea µ ad stadard deviatio σ the σ X N(µ, ) 3. Law of Large Nubers As gets larger ad larger, X gets closer ad closer to µ. 4. Cetral Liit Theore: If X 1,..., X coe fro a distributio with ea µ ad stadard deviatio σ, the σ X N(µ, ) for large.

3 CH14: Itroductio to Iferece 1. Defiitio of a α level cofidece iterval. estiate ± error 2. Iterpretatio of a α level cofidece iterval: We are α % sure that the true value of the paraeter lies i the cofidece iterval. 3. Cofidece iterval for µ whe σ is kow: X ± Z σ 4. Defiitio of p-value 5. Hypothesis Testig: Geeric Method (a) Write dow defiitio of p-value i ters of the test statistic (b) Stadardize the test statistic (c) Recogize the distributio after stadardizatio (d) Look up the probability i the appropriate table or use software. (e) Check p-value agaist sigificace level ad decide whether or ot to reject. If p is saller tha sigificace: Reject H 0 ; Otherwise: Caot reject. CH 15: Thikig about Iferece 1. Be failiar with how cofidece Itervals behave. 2. Kow the differece betwee Type 1 ad Type 2 error. 3. Be able to fid the Type 2 error give the power of the test. 4. Saple size for desired argi of error. = z σ 5. Perforig hypothesis test for µ whe σ is kow. CH18: Oe Saple t procedures: Iferece for the ea whe σ is ukow. 1. Coditios for t test: (a) Observatios have a oral distributio with ea µ ad st. dev σ, which are ukow.

4 (b) Observatios coe fro a distributio with ea µ ad st. dev σ, which are ukow, the distributio is roughly syetric without outliers. 2. Oe saple t statistic: X µ 0 S/ t( 1) 3. Cofidece iterval of size α for µ whe σ is ukow: X ± t S 4. Hypothesis Tests for µ whe σ is ukow. CH19: Two Saple t procedures. 1. Iferece for µ x µ y 2. Two-Saple t statistic: t = X Ȳ s 2 x + s2 y t(i( 1, 1)) 3. Cof Iterval for µ x µ y : X Ȳ ± t s 2 x + s2 y t is the α Critical value fro the t(i( 1, 1)) 4. Hypothesis tests for µ x = µ y i.e. µ x µ y = 0. CH20: Iferece About populatio proportios. 1. Defiitio of ˆp Nuber of Successes ˆp = Saple Size p(1 p) 2. Distributio of ˆp N(p, ) 3. Cof. Iterval for p CH23: χ 2 test ˆp ± Z ˆp(1 ˆp)

5 1. Expected Couts: RowTotal x ColuTotal Saple Size p i,0 2. χ 2 Statistic χ 2 = (Observed Expected) 2 Expected χ 2 ((r 1)(c 1)) Where the su is take over all cells i the two way table. χ 2 = (Observed i p i,0 ) 2 p i,0 χ 2 (k 1) Where the su is take over all k cells i the distributio table. CH25: ANOVA 1. Kow how ad whe to use the ANOVA test. 2. Kow how to read a ANOVA coputer output. 3. Kow how to ake cofidece itervals usig the pooled stadard deviatio.

Chapter 10 - Lecture 2 The independent two sample t-test and. confidence interval

Chapter 10 - Lecture 2 The independent two sample t-test and. confidence interval Assumptios Idepedet Samples - ukow σ 1, σ - 30 or m 30 - Upooled case Idepedet Samples - ukow σ 1, σ - 30 or m 30 - Pooled case Idepedet samples - Pooled variace - Large samples Chapter 10 - Lecture The