MATH 2500 - Introduction to Statistics

• Carry out a hypothesis test for a mean or proportion. Interpret statistical and practical significance in this setting.
• Compute conditional probabilities in the context of two-way tables.
• Construct a model for a random phenomenon using outcomes, events, and the assignment of probabilities. Use the addition rule for disjoint events and the multiplication rule for independent events.
• Determine the appropriate sample size for a specific margin of error and confidence level.
• Estimate a population mean or proportion using a point estimate and confidence intervals, and interpret the confidence level and margin of error.
• Given a research question involving a single population, formulate null and alternative hypotheses. Describe the logic and framework of the inference of hypothesis testing.
• Introduce the concept of a sampling distribution. Discuss the distribution of the sample mean and sample proportion under repeated sampling (Central Limit Theorem).
• Investigate and describe the relationships or associations between two variables using caution in interpreting correlation and association.
• Make a decision using a p-value and draw an appropriate conclusion. Interpret statistical significance.
• Perform interval estimation and hypotheses testing for two-sample problems (e.g., difference of two means or proportions and chi-square test of independence).
• Select and produce appropriate graphical, tabular, and numerical summaries of the distributions of variables in a data set. Summarize such information into verbal descriptions.
• Students should be expected to simulate or generate sampling distributions to observe, empirically, the Central Limit Theorem.
• Summarize relationships in bivariate data using graphical, tabular, and numerical methods including scatter plots, two-way tables, correlation coefficients, and least squares regression lines.
• Understand how the type of data collection can affect the types of conclusions that can be drawn.
• Understand the dependence of margin of error on sample size and confidence level.
• Understand the principles of observational and experimental studies including sampling methods, randomization, replication, and control.
• Use the normal distribution to interpret z-scores and compute probabilities.