Question

Describe tests we might conduct based on Data 2.3 , introduced on page \(69 .\) This dataset, stored in ICUAdmissions, contains information about a sample of patients admitted to a hospital Intensive Care Unit (ICU). For each of the research questions below, define any relevant parameters and state the appropriate null and alternative hypotheses. Is there a difference in the proportion who receive CPR based on whether the patient's race is white or black?

Short answer

The relevant parameters are the proportions of white patients (\( p_{1} \)) and black patients (\( p_{2} \)) who receive CPR. The Null Hypothesis is \( H_{0} : p_{1} = p_{2} \) implying there is no difference in the proportions of white and black patients receiving CPR. The Alternative Hypothesis is \( H_{1} : p_{1} ≠ p_{2} \) implying there is a difference. The appropriate test is a two-proportion z test.

Step-by-step solution

Understanding the Task

Data 2.3, consists of data about various patients admitted to a hospital's ICU. The task attempts to find out if there is a difference in the proportion of patients who receive CPR based on their race - white or black.

Identify Parameters

Parameters are important quantities in populations that we want to estimate or test. In this case, the parameters are the proportions of white and black patients who receive CPR. Let's use \( p_{1} \) to represent the proportion of white patients who receive CPR and \( p_{2} \) to represent the proportion of black patients who receive CPR.

State the Null Hypothesis

The Null Hypothesis usually states there is no effect or no difference in our case of comparison. Thus our null hypothesis will be: \( H_{0} : p_{1} = p_{2} \) which means there is no difference in the proportions of white and black patients receiving CPR.

State the Alternative Hypothesis

The Alternative Hypothesis is the contrary to what the null hypothesis assumes. It often states there is an effect or a difference. Thus our alternative hypothesis would be \( H_{1} : p_{1} ≠ p_{2} \), indicating there is a difference in the proportions of white and black patients receiving CPR.

Chose Appropriate Test

We have two populations (white and black patients) and we are comparing their proportions (those who receive CPR). The appropriate test in this scenario would be a two-proportion z test.