MA 2410 - Statistics for AS

• Choose which probability distribution applies to a given statistical situation
• Perform a complete hypothesis test
• Correctly calculate and interpret a p-value
• Recognize the similarities between the various hypothesis tests and the formulas used by these tests
• Construct estimators using method of moments and maximum likelihood estimator
• Demonstrate understanding of sampling distributions
• Perform analysis of variance when appropriate and interpret the results
• Describe properties of estimators, including mean squared errors and UMVUE
• Apply Neyman-Pearson Lemma and likelihood ratio tests
• Construct confidence intervals for mean, the difference of two means, the difference of proportions and variance 
• Apply analysis of variance and chi-square goodness-of-fit tests

• Differential and integral calculus (both single and multivariable)

• Major probability distributions used in hypothesis testing including normal, student-t, chi-square, and F
• Sampling distribution and central limit theorem
• Constructing estimators using such as the method of moments and maximum likelihood estimator 
• Properties of estimators, including mean squared errors and UMVUE
• Theory of hypothesis test, including Neyman-Pearson Lemma and likelihood ratio test
• One-sample and two-sample hypothesis testing
• Confidence intervals for mean, the difference of two means, the difference of proportions and variance
• Analysis of variance and chi-square goodness-of-fit test