Class Activity, February 22

Hypothesis testing with the Titanic data

In this class activity, we will construct confidence intervals for quantities of interest in the titanic data. Let \(Y_i\) denote whether passenger \(i\) survived. We will use the model

\[Y_i \sim Bernoulli(p_i)\]

\[\log \left( \dfrac{p_i}{1 - p_i} \right) = \beta_0 + \beta_1 Sex_i + \beta_2 Age_i + \beta_3 SecondClass_i + \beta_4 ThirdClass_i\]

The Titanic data can be imported into R with

titanic <- read.csv("https://sta711-s23.github.io/homework/Titanic.csv")

Part I

  1. Fit the logistic regression model in R.

  2. Use a Wald test to test

\[H_0: \beta_3 = \beta_4 = 0 \hspace{1cm} H_A: \text{at least one of } \beta_3, \beta_4 \neq 0\]

Part II

  1. Use a Wald test to test

\[H_0: \beta_4 - \beta_3 = 0 \hspace{1cm} H_A: \beta_4 - \beta_3 \neq 0\]