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Statistics and Probability Tutoring Topics


Our Statistics and Probaility Tutoring includes all topics covered in High School Statistics and AP Statistics as well as College Level. Our instruction also prepares students for the College Board AP Statistics Course thru our sessions. Below are the topics

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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

Statistics Calculation 2

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


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