# STAT 319: Applied Statistics in Science

#### Spring 2013

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

• $$E(\bar{X})$$
• $$V(\bar{X})$$
• [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

• t-distn, F-ditrn, chisq-distn
Jan. 23 Lec 6.4 (cont.) Quiz 1
Jan. 25 Lec 7.1
• 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)
• Def: population moment, sample moment
• Method: Method of moments. (5 steps)
Feb. 1 Lec 7.2 (MLE)
• Method: Maximum likelihood estimation. (5 steps)
Feb. 4 Lec 7.2 (MLE), Bootstrap
• speical case for MLE.
• Bootstrap method to find standard errors.
Feb. 6 Lec 8.1
• CI for normal population with sigma known.
• sample size calculation.
Feb. 8 Lec Recap for Midterm 1
Feb. 11 Lec 8.2 (1)
• CI for general population with large sample size.
• One-sided CI
Feb. 13 Midterm 1
Feb. 15 Lec 8.2 (1) cont., (2)
• CI for proportion with large sample size.
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
• 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

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

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

Mar. 15 Lec 10.1

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

Mar. 18 Lec 10.1 (cont.)

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

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

Apr. 3 Lec 10.3

Apr. 5 Lec 11.1

Apr. 8 Lec 11.1 (cont.)

Apr. 22 Lec 12.3 Inference on $$\beta_1$$ : distiribution of $$\hat{\beta}_1$$, confidence interval and hypothesis testing.