The course "Statistics II" aims to familiarize students with special topics and specialized statistical methodologies. First, an introduction to statistics is given, presenting basic concepts taught during the course "Statistics I". Students are then introduced to descriptive statistics, statistical functions, point estimates and hypothesis testing. Lectures conclude with analysis of variance and χ²

1^th Lecture: Introduction

• Review basic probability concepts and connect probability with statistics

2ⁿ – 4ⁿ Lecture: Descriptive Statistics

• Quantitative variables
  • Construction of frequency (distribution) table
  • Graphical presentation of frequency distribution
  • Numerical descriptive measures
  • Position measures
  • Dispersion measures
  • Measures of skewness and measures of kurtosis
• Qualitative variables
• Direction and direction variables
• Frequency distribution plot of circular data
• Numerical descriptive measures of circular data

5^h – 7^h Lecture: Statistical Functions and Sampling Distributions

• Basic Concepts
• Basic Sampling Distributions
• Estimating Functions and Estimation Methods
• Point Estimation and Confidence Interval Estimation
  • Properties of estimators
• Confidence interval for the population mean
• Confidence interval for the binomial proportion
• Confidence interval for the variance of a normal population
• Confidence Interval for the Difference of Two Population Means (Independent and Dependent Samples)
• Confidence Interval for the Difference of Two Binomial Proportions with Two Independent Samples
• Confidence interval for the ratio of the variances of two normal populations
• Upper and lower limits of a confidence interval

8^h – 10^h Lecture: Statistical hypothesis testing

• Basic concepts
• Statistical hypothesis testing about the mean of a population
  • The population is normal
  • The size of the sample is large
• Type II error probability and power of a test statistic
• Statistical hypothesis testing for the binomial rate
• Statistic hypothesis testing for the variance of a normal population
• Statistical hypothesis testing for the difference of two population means (independent and dependent samples)
• Statistical hypothesis testing for the difference of two binomial proportions with two independent samples
• Statistical testing of hypotheses for the equality of variances of two normal populations Basic discrete distributions

11^h – 12^h Lecture: Analysis of Variance

• Completely Randomized Design
  • (1 – a)100% Confidence Intervals for the Mean of One Operation and for the Difference of Means of Two Operations
  • Multiple comparison controls
  • Assumptions/assumptions in completely randomized design
• Randomized Complete Group Design
  • Multiple Comparison Tests
  • Assumptions/Assumptions
• a X b Factorial Experiment
  • Multiple Comparison Tests
  • Interaction diagram
  • Assumptions/assumptions in a X b factorial experiment with r > 1 observation per operation

13^h Lecture: χ²

• Chi² test of goodness of fit with and without unknown parameters
• Chi² test of independence

χ² homogeneity test