Guaranteed B+ or Better in MATH 120

Week 1 introduces the fundamentals of statistics including types of data (qualitative vs quantitative, discrete vs continuous), sampling methods, and measures of central tendency (mean, median, mode). You'll learn to create and interpret frequency distributions, histograms, stem-and-leaf plots, and box plots. This week establishes the vocabulary and basic concepts that underpin all statistical analysis. Students often struggle with distinguishing between population parameters and sample statistics, and with choosing appropriate graphs for different data types. We provide clear examples of each concept and help you understand when to use each measure and visualization technique for effective data communication.

Week 2 builds on descriptive statistics by introducing measures of spread including range, variance, and standard deviation. You'll learn to calculate and interpret these measures, understand the empirical rule for normal distributions, and use z-scores to identify unusual values. The week also covers percentiles, quartiles, and the five-number summary. Quiz 1 tests your understanding of Weeks 1-2 material. Common difficulties include confusing population and sample formulas for variance, misinterpreting standard deviation values, and calculating z-scores incorrectly. Our tutoring emphasizes the practical meaning of these measures and provides strategies for remembering which formulas to use in different contexts.

Week 3 introduces probability theory including basic probability rules, complementary events, addition rule, and multiplication rule for independent and dependent events. You'll learn to calculate conditional probabilities and understand the difference between mutually exclusive and independent events. The week includes applications like calculating odds and expected value. Students frequently confuse independence with mutual exclusivity, make errors with the multiplication rule for dependent events, and struggle with conditional probability notation. We break down each probability rule with clear examples and provide decision trees to help you determine which rule applies to each problem type.

Week 4 covers discrete random variables, probability distributions, expected value, and variance of discrete distributions. You'll master the binomial probability distribution including when to use it, how to calculate binomial probabilities, and how to find mean and standard deviation. The week includes applications like quality control and survey analysis. Quiz 2 covers Weeks 3-4 material. Common challenges include identifying when a situation follows a binomial distribution, using the binomial probability formula correctly, and interpreting expected value in context. Our tutoring provides a checklist for binomial conditions and extensive practice with real-world applications to build your intuition.

Week 5 introduces continuous probability distributions, focusing on the normal distribution and its properties. You'll learn to use z-scores and normal distribution tables to find probabilities and percentiles, understand the Central Limit Theorem and its implications, and work with sampling distributions of sample means. This is crucial material that forms the foundation for inferential statistics. Students often struggle with converting between raw scores and z-scores, using the normal table correctly, and understanding when the Central Limit Theorem applies. We provide step-by-step processes for normal probability problems and clear explanations of why the Central Limit Theorem is so powerful in statistics.

Week 6 marks the transition to inferential statistics with confidence intervals for population means and proportions. You'll learn to construct and interpret confidence intervals, understand the relationship between confidence level and interval width, and determine appropriate sample sizes. The week covers both z-intervals (when population standard deviation is known) and t-intervals (when it's unknown). Quiz 3 tests Weeks 5-6 material. Common errors include confusing confidence level with confidence interval, misinterpreting what a confidence interval tells us, and using the wrong distribution (z vs t). Our tutoring emphasizes the correct interpretation of confidence intervals and provides clear decision rules for choosing between z and t procedures.

Week 7 introduces hypothesis testing including null and alternative hypotheses, Type I and Type II errors, significance levels, p-values, and test statistics. You'll learn to conduct hypothesis tests for population means and proportions using both critical value and p-value methods. The week includes one-tailed and two-tailed tests and emphasizes proper conclusions in context. Students frequently struggle with stating hypotheses correctly, interpreting p-values, and drawing appropriate conclusions. We provide templates for hypothesis test procedures and help you understand the logic behind statistical significance, ensuring you can explain your conclusions in plain language that makes sense in the problem context.

Week 8 covers linear regression and correlation including scatter plots, correlation coefficient, regression equations, and making predictions. You'll learn to interpret the slope and y-intercept in context, assess the strength of linear relationships, and understand the limitations of regression analysis. The comprehensive final exam covers all material from Weeks 1-7 with emphasis on probability, normal distribution, confidence intervals, and hypothesis testing. Students often confuse correlation with causation and make errors in regression predictions outside the data range. We provide a complete final exam review focusing on the most commonly tested concepts and problem types, with special attention to the conceptual questions that often appear on the exam.