STAT 319: Applied Statistics in Science

Spring 2013

Syllabus    Lectures    Computing    Assignments    Readings    Calendar     Announcement   
Lecture Date Covered Notes
Jan. 7 Welcome to STAT 319 !    Review STAT 318. Memo: Version of books and some students have books ship in the way. Rules about project.
Jan. 9 Lec 6.1

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  • Definition: random variable/observation, random sample, statistics, sampling distribution
  • Computation: finding sampling distribution for \( \bar{X} \)and \( S^2 \).
Jan. 11 Lec 6.3

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  • Definition: linear combination
  • Four proposition:
    • Prop 1: \( E(\sum_{i=1}^n a_i X_i) \)
    • Prop 2: \( V(\sum_{i=1}^n a_i X_i) \)
    • Prop 3: liear comb of normal r.v.s are still normally distributed.
    • Prop 4: property about moment generating function.
  • Computation: based on proposition 1-3
  • Proof: based on proposition 4
Jan. 14 Lec 6.2

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  • \( E(\bar{X}) \)
  • \( V(\bar{X}) \)
  • [LLN] \( \bar{X} \rightarrow \mu \) as \(n \rightarrow \infty \)
  • Distn of \( \bar{X} \) when \(X_i\) are random sample from Normal distribution.
Jan. 16 Lec 6.2(cont.)
  • [CLT] Asymptotic distrn of \( \bar{X} \)
Jan. 18 Lec 6.4

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  • t-distn, F-ditrn, chisq-distn
Jan. 23 Lec 6.4 (cont.) Quiz 1
Jan. 25 Lec 7.1

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  • Estimator, Estimate, Parameter
  • Unbiasedness, MVUE, Minimum MSE
Jan. 28 Lec 7.1 (cont.)

Working through more examples for topics in Lec 7.1. For example, how to find unbiased estimators and how to calcualte mean square errors.

Jan. 30 Lec 7.2 (MOM)

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  • Def: population moment, sample moment
  • Method: Method of moments. (5 steps)
Feb. 1 Lec 7.2 (MLE)

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  • Method: Maximum likelihood estimation. (5 steps)
Feb. 4 Lec 7.2 (MLE), Bootstrap

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  • speical case for MLE.
  • Bootstrap method to find standard errors.
Feb. 6 Lec 8.1

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  • CI for normal population with sigma known.
  • sample size calculation.
Feb. 8 Lec Recap for Midterm 1
Feb. 11 Lec 8.2 (1)

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  • CI for general population with large sample size.
  • One-sided CI
Feb. 13 Midterm 1
Feb. 15 Lec 8.2 (1) cont., (2)

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Feb. 18 Lec 8.3

CI for Normal population with unknown variance under samll sample size Notes download here

Feb. 20 Lec 8.3 (cont.) + summary of chapter 8
Feb. 22 Lec 9.1

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  • Hypothesis testing procedures.
  • Rules of specifying the H0 and H1. Type I, II error.
Feb. 25 Lec 9.1 (cont.)
Feb. 27 Lec 9.2

Hypothesis testing for population mean. Notes download here

Mar. 1 Lec 9.2 (cont.)
Mar. 11 Lec 9.3

Hypothesis testing for population proportion. Notes download here ( updated )

  • Large sample case: approximate z test.
  • Small sample case: directly based on Binomial distribution.
Mar. 13 Lec 9.4

P-values Notes download here

Test outputs from various softwares

Mar. 15 Lec 10.1

Tests and Con dence Intervals for a Difference between two population means

Normal sample Notes download here

Mar. 18 Lec 10.1 (cont.)

Tests and Con dence Intervals for a Difference between two population means

Genearl sample with large sample size Notes download here

Mar. 20 Lec 10.2

The independent two sample t-test and con dence interval Notes download here

  • Pooled variance case.
  • Unpooled variance case.
Mar. 22 Review for midterm 2.
Mar. 25 Lec 10.2 (cont.)
Mar. 27/29 Midterm 2
Apr. 1 Lec 10.4

Inference about two population proportions Notes download here

Apr. 3 Lec 10.3

Analysis of Paired data Notes download here

Apr. 5 Lec 11.1

Single Factor ANOVA Notes download here

Apr. 8 Lec 11.1 (cont.)

More on Single Factor ANOVA Notes download here

Apr. 10 Lec 11.2

Multiple comparisions in Single Factor ANOVA Notes download here

Apr. 12 General intro to regression.
Apr. 15 Lec 12.1 Intro to the simple linear regressions: model and the assumptions.
Apr. 17 Lec 12.2 Estimating model parameters
Apr. 19 Lec 12.2 (cont.) Regression and ANOVA
Apr. 22 Lec 12.3 Inference on \( \beta_1 \) : distiribution of \( \hat{\beta}_1 \), confidence interval and hypothesis testing.
Apr. 24 Work through problems of chapter 12.
Apr. 26 Review for final exams.