Study Guide for Final Quiz (Aug 11th)

The Quiz 2 will cover Chpater 1-8, Lecture note 1-18, with an emphasis on Chpater 1-4, Lecture note 11-18

Note: One page(one-sided) cheat sheet will be allowed for Quiz 2. You can write down the formula such as sampling standard deviation.

Primary resources (desceding order by importance)

Lecture notes with emphasis on
- How do we define each concept?
- Practice questions – reasoning for every options(why correct? why wrong?)
R Session code with emphasis on
- Why are we running this code? What do we want to check by running the code?
- What does specific code mean? Which element is needed for running a sepcific function?
Recommended exercises in OS
- Emphasis on how the related concepts can be used in real-life example
Sample quiz
- Thoroughly review lecture notes, R code and practice questions from the textbook prior to working on the sample quiz

Chapter 1. Introduction to data

Learning Objective

Variable Types: Numerical vs. Categorical/ Response vs. Explanatory/ Obervational vs. Experimental
Sampling method: Simple random sampling, Cluster sampling, Stratified sampling
Causation vs. Correlation/Association

Resource

Lecture note

Exercises

(p.11) Exercise 1.2: Sinusitis and antibiotics
(p.19) Exercise 1.5: Cheaters, study components
(p.20) Exercise 1.8: Sinusitis and antibiotics Part II
(p.31) Exercise 1.27: Sampling strategies
(p.35) Exercise 1.30: Vitamin Supplements
(p.36) Exercise 1.37: Chia seeds and weight loss
(p.37) Exercise 1.39: Flawed reasoning
(p.37) Exercise 1.41: Eat better, feel better

R Session

How do we use the following packages: tidyverse, ggplot2?
[arbuthnot]Interpret the trend on the number of new born boys/girls.

Chapter 2. Summarizing the data

Learning Objective

Numerical Data
- Graphical Summary: Histogram, Boxplot, Scatterplot
- Numerical Summary: Mean and Variance
Categorical Data: Frequnecy table, Contingency table, Barplot, Mosaic plot
Overview for Hypothesis Testing(Malaria vaccine)

Resource

Lecture note

Special emphasis on the simulation for malaria vaccine
Sec 2.3. Case study: malaria vaccine

Exercises

(p.56) Exercise 2.2: Associations
(p.56) Exercise 2.5: Parameters and statistics
(p.57) Exercise 2.10: Mix-and-match
(p.58) Exercise 2.12: Median vs. Mean
(p.70) Exercise 2.24: Raise taxes
(p.76) Exercise 2.26: Heart transplants
(p.77) Exercise 2.31: Oscar winners
(p.78) Exercise 2.34: Marathon winners

R Session

The important part is
- why this particular graph is useful in summarizing the data
- how to interpret the graph

Chapter 3. Proabibility

Learning Objective

Definition of Probability: Frequentist vs. Bayesian
Law of Large Numbers
Independent vs. Disjoint vs. Complementary
Product rule for independent Events: $P(A \cap B) = P(A) \times P(B)$
General addition rule: $P(A \cap B) = P(A) + P(B) - P(A \cap B)$
Sampling with, without replacement

Resource

Lecture note

Exercises

(p.92) Exercise 3.1: Ture or false
(p.92) Exercise 3.5: Coin flips
(p.93) Exercise 3.9: Disjoint vs. independent
(p.109) Exercise 3.13 (a), (b)-i, (b)-ii, (c)
(p.114) Exercise 3.23: Marbles in an urn
(p.114) Exercise 3.27: Student outfits
(p.124) Exercise 3.29: College smokers
(p.124) Exercise 3.31: Heart win
(p.129) Exercise 3.40: Health coverage, frequencies
(p.130) Exercise 3.44: Scooping Ice cream

R Session

Special emphasis on Law of Large Numbers simulation

Chapter 4. Distributions of Random Variables

Learning Objective

Normal Distribution
- Parameters: \mu(mean), \sigma(standard deviation)
- Calculate the probability using pnorm
- Calculate the percentile using qnorm
- Z-score and standard normal distribution
Bernoulli Distribution: Milgram experiment
Binomial Distribution
- Parameters: n(the number of trials), p(probability of success)
- Normal approximation to binomial distribution
Poisson Distribution

Resource

Lecture note

Sec 4.5. Poisson distribution – to see the examples potentially following poisson distribution

Exercises

(p.142) Exercise 4.3: GRE scores, Part I – use pnorm to calculate the probability
(p.142) Exercise 4.5: GRE scores, Part II – use qnorm to calculate the percentile
(p.148) Exercise 4.11: Is it Bernoulli?
(p.148) Exercise 4.12: With and without replacement
(p.157) Exercise 4.22: Arachnophobia
(p.166) Exercise 4.27: University admissions
(p.166) Exercise 4.39: Auto insurance premiums

R Session

Emphasis on the usage of pnorm
Distinguish when to use pnorm and qnorm

Chapter 5. Introduction to Inference

Learning Objective

Point estimate and sampling variability
- Understand the sampling variability
- Central Limit Theorem
Confidence interval
- Interpretation of confidence interval
Hypothesis testing for a proportion

Resource

Lecture note-Part I

Lecture note-Part II

Exercises

(p.179) Exercise 5.3: Quality control
(p.188) Exercise 5.12: Mental Health
(p.202) Exercise 5.15: Identify hypotheses, Part I
(p.202) Exerecise 5.16: Identify hypotheses, Part II
(p.202) Exercise 5.19: Cyberbullying rates
(p.203) Exercise 5.25: Testigng for Fibromyalgia
(p.204) Exercise 5.29: Testing for food safety

R Session

Emphasis on the calculation of p-value

Chapter 6. Inference for Categorical Data

Learning Objective

Inference for a single proportion
Difference of two proportions

Resource

Lecture note

Exercises

(p.215) Exercise 6.9: Study abroad
(p.216) Exercise 6.10: Legalization of marijuana, Part I
(p.225) Exercise 6.18: Heart transplant success
(p.228) Exercise 6.28: Prenatal vitamins and Autism
(p.247) Exercise 6.45: Life after college

R Session

Interpret the result from t.test

Chapter 7. Inference for Numerical Data

Learning Objective

Test for Mean Determine when to use normal distribution/t-distribution?
- Large sample: normal distribution
- Population distribution is normal: normal distribution
- Neither case: t-distribution
One-sample mean with t-distribution
Paired data vs. Difference in two means