### Statistics and Probability Tutoring Topics

*"Gary is very knowledgeable, patient, and clear in explaining concepts. He was great preparing my son for exams and finals. And my son completed his math requirement at De Anza College successfully. My son is now attending a 4-year college and he is doing really well. Gary played a big part in his success."*S. Hamill, Cupertino

**Confidence Intervals and Introduction to Inference**

Estimation, Confidence Intervals, tProcedures, Choosing a Sample Size for a Confidence Interval, P-Value, Statistical Significance, Hypothesis Testing Procedure, Errors in Hypothesis Testing,

**The Power of a Test**

Statistical Inference: Estimating population parameters and testing hypotheses

**Estimation **

Estimation (point estimators and confidence intervals), Estimating population parameters and margins of error, Properties of point estimators, including unbiasedness and variability, Logic of confidence intervals, meaning of confidence level and confidence, intervals, and properties of confidence intervals, Large sample confidence interval for a proportion, Large sample confidence interval for a difference between two proportions, Confidence interval for a mean, Confidence interval for a difference between two means (unpaired and paired), Confidence interval for the slope of a least-squares regression line

**Sampling distributions**

Sampling distribution of a sample proportion, Sampling distribution of a sample mean, Central Limit Theorem, Sampling distribution of a difference between two independent sample proportions, Sampling distribution of a difference between two independent sample means, Simulation of sampling distributions, t-distribution, Chi-square distribution

**Inference for Means and Proportions**

The Logic of Hypothesis Testing. zProcedures vs. tProcedures, Inference for a Population Mean, Inference for the Difference between Two Population Means, Inference for a Population Proportion, Inference for the Difference between Two Population Proportions

**Tests of significance**

Logic of significance testing, null and alternative hypotheses; p-values; one- and two-sided tests; concepts of Type I and Type II errors; concept of power, Large sample test for a proportion, Large sample test for a difference between two proportions, Test for a mean, Test for a difference between two means (unpaired and paired), Chi-square test for goodness of fit, homogeneity of proportions, an independence (one- and two-way tables), Test for the slope of a least-squares regression line

**Inference for Regression**

Simple Linear Regression (Review), Significance Test for the Slope of a Regression Line, Confidence Interval for the Slope of a Regression Line, Inference for Regression using Technology

**Inference for Categorical Data:
**Chi-Square, Chi-square Goodness-of-Fit Test, Chi-square Test for Independence, Chi-square Test for Homogeneity of Proportions (Populations), χ2 vs.z2

**Overview of Statistics/ Basic Vocabulary**

The Meaning of Statistics, Quantitative vs. Qualitative Data, Descriptive vs. Inferential Statistics, Collecting Data, Experiments vs. Observational studies, Random Variables

**One-Variable Data Analysis**

Shape of a Distribution, Dotplot, Stemplot, Histogram, Measures of Center, Measures of Spread, 5-number Summary, Boxplot, z-score, Density Curve, Normal Distribution, The Empirical Rule, Chebyshev’s Rule

Constructing and interpreting graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot), Center and spread , Clusters and , Outliers and other unusual features, Shape , Summarizing distributions of univariate data , Measuring center: median, mean Measuring spread: range, interquartile range, standard deviation, .Measuring position: quartiles, percentiles, standardized scores (z-scores) Using boxplots , The effect of changing units on summary measures

Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots), Comparing center and spread: within group, between group variation, Comparing clusters and gaps, Comparing outliers and other unusual features, Comparing shapes

**Two-Variable Data Analysis**

Analyzing patterns in scatterplots, Lines of Best Fit, The Correlation Coefficient, Least Squares Regression Line, Coefficient of Determination, Residuals, Outliers and Influential Point, Transformations to Achieve Linearity

**Design of a Study: Sampling, Surveys, and Experiments**

Samples and Sampling, Surveys, Sampling Bias, Experiments and Observational Studies, Statistical Significance, Completely Randomized Design, Matched Pairs Design, Blocking, Random Variables and Probability, Probability, Random Variables, Discrete Random Variables, Continuous Random Variables, Probability Distributions, Normal Probability, Simulation, Transforming and Combining Random Variables

**Overview of methods of data collection**

Characteristics of a well-designed and well-conducted survey, Populations, samples and random selection, Sources of bias in sampling and surveys, Sampling methods, including simple random sampling, stratified random sampling and cluster sampling, Planning and conducting experiments, Characteristics of a well-designed and well-conducted experiment, Treatments, control groups, experimental units, random assignments and replication Sources of bias and confounding, including placebo effect and blinding, Completely randomized design, Randomized block design, including matched pairs design

**Probability**

Interpreting probability, including long-run relative frequency interpretation, “Law of Large Numbers” concept, Addition rule, multiplication rule, conditional probability and independence, Discrete random variables and their probability distributions, including, binomial and geometric, Simulation of random behavior and probability distributions, Mean (expected value) and standard deviation of a random variable, and linear transformation of a random variable

**Combining independent random variables**

Independence versus dependence, Mean and standard deviation for sums and differences of independent, random variables, The normal distribution, Properties of the normal distribution, Using tables of the normal distribution, The normal distribution as a model for measurements

**Need to some practice, here is the 2012 AP Statistics Exam **

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