Various numerical assignments from STAT 30040 (Statistical Theory and Methods IIa), taught by Dr. Mei Wang, at UChicago.
- In Homework 2, Exercise 1, we examine how to approximate probabilities under the binomial distribution using the Poisson and normal distributions. In Exercise 4, we compare the coverage probabilities of various asymptotic confidence intervals, including those constructed with the Wald, Wilson, and variance stabilization methods.
- In Homework 4, Exercise 2, we perform a likelihood ratio test to assess the null hypothesis that the probability of the Dow Jones having an "up" day during the first half of the 20th century was equal to the corresponding probability during the second half of the 20th century, assuming the distribution of up days was binomial during each half century. In Exercise 4, we manually walk through the mechanics of a simple one-way ANOVA.
- In Homework 5, we explore more complex aspects of ANOVA, including two-way ANOVAs with and without interaction terms, the relationship between two-way and one-way ANOVAs, the limitations of ANOVA in the absence of treatment replication, and sequential ANOVA.