In addition to the general purposes of the mathematics department (stated separately), the specific purposes of this course involve introducing students to four major statistical themes.
1. Exploratory analysis of data making use of graphical and numerical techniques to study patterns and departures from patterns.
2. The realization that data must be collected according to a well developed plan if valid information on a conjecture is to be obtained.
3. The realization that probability is a valuable tool for anticipating what the distribution of data should look like under a given model.
4. The fact that models and data interact in statistical work. Models are used to draw conclusions from data. Inference from data is a process of selecting a reasonable model, including a statement in probability language, of how confident one can be about the selection.
A. Interpreting graphical displays
1. Center and spread
2. Clusters and gaps
3. Outliers and other unusual features
B. Summarizing distributions of univariate data
1. Measuring center: mean, median, mode
2. Measuring spread: range, interquartile range, standard deviation
3. Measuring position: quartiles, percentiles, z-scores
5. effect of changing units on summary measures
C. Comparing distributions of univariate data
1. Dotplots, back-to-back stemplots, parallel boxplots
2. Comparing center and spread between groups
3. Comparing clusters and gaps
4. Comparing shapes
D. Exploring bivariate data
1. Analyzing patters in scatterplots
2. Correlation and linearity
3. Least-squares regression line
4. Residual plots, outliers, influential points.
5. Logarithmic transformations
E. Exploring categorical data: frequency tables
1. Marginal and joint frequencies for 2-way tables
2. Conditional relative frequencies and association
A. Overview of data collection methods
2. Sample survey
4. Observational study
B. Planning and conducting surveys
C. Planning and conducting experiments
D. Generalization of results from observational studies, experimental studies, and surveys
A. Probability as relative frequency
1. Law of large numbers.
2. Probability rules for addition and multiplication
3. Concept of independence and disjoint
4. Discrete random variables, including binomial
5. Simulation of probability distributions
6. Mean and standard deviation of random variable
B. Normal distribution
1. Properties of normal distribution
2. Using tables and calculator with normal distribution
3. Normal distribution as a model
C. Sampling distributions
1. Sampling distribution of a sample proportion
2. Sampling distribution of a sample mean
3. Central Limit Theorem
A. Confidence intervals
1. Meaning of confidence interval
2. Large sample confidence interval for a proportion
3. Large sample confidence interval for a mean
B. Tests of significance
1. Significance testing, null and alternate hypotheses
2. Large sample test for a proportion
3. Large sample test for a mean
4. Chi-square test for goodness of fit
C. Special case of normally distributed data
1. t distribution
2. Single sample t procedures.