Question

1.) A large hospital in the Midwest, with more than 30,000 patients in a year, is interested in how long a patient had to wait from when they made the appointment to when they were seen. The hospital director is interested in learning this information so they can identify what section has the longest wait time and devote more resources to fix the problem. As such, the hospital director is going to sample from patients it has had in the last year to learn about wait times.
The hospital has several ways in which it can sample. The hospital was made up of 21 different ”wings”. Examples include the psychiatric wing, the oncology wing, the cardiology wing, etc.... The hospital also have doctors who work only in one wing of the hospital, with at least a few doctors in each wing. You may assume that there is roughly an equal amount of patients in each wing, and that the number of patients seen by each doctor is roughly the same. Assume the patient only was ever in one wing of this hospital.
On the next page is a small table to give you an idea of how the hospital is set up. Not all wings are listed nor are all doctors listed. This is just to help you visualize the set up.
How should the hospital sample in order to get a simple random sample, a cluster sample and a stratified sample? That is the goal of this section of the test. For each of the following, please write at least a small paragraph worth for each sampling plan. You need to be very specific in your response. There should be no ambiguity of how you will sample from the patients. Your responses need to be written in the answers.pdf file.
1. How should the hospital sample to get a Simple Random Sample?
2. How should the hospital sample to get a Cluster Sample?
3. How should the hospital sample to get a Stratified Sample?
4. Which do you think is the most correct method, especially given the hospital’s goals?

Answer 1

1. How should the hospital sample to get a Simple Random Sample?

For the given scenario regarding the waiting time of patients, we will get a simple random sample of the patients waiting time by drawing a random sample from the entire data available for the waiting times for patients. We will take the list of all patients including waiting times for defined time period. We will assign the numbers for Patient ID’s from 1 to N. Then we will select the random sample of size n from given population with size N. For this scenario, the population size (N) would be more than 30000. We will include at least 10% of population size in the selected random sample. This means, the sample size of a selected random sample would be more than 300 approximately. If sample size for selected random sample is not adequate, then we will get biased results for this study.

2. How should the hospital sample to get a Cluster Sample?

We are given that there are total 21 different wings in the given hospital. We know that the size of patients in each wing is approximately same. This means data is scattered homogeneously between different wings. We will select some wings out of given 21 wings by using random sampling. After the selection of random wings, we will include all patients from these selected wings for this research study. We will include selected entire clusters in the research study. This will give us a cluster sample.

3. How should the hospital sample to get a Stratified Sample?

For getting a stratified random sample, we will consider each wing of the hospital as a single stratum. Then we will use simple random sampling for the selection of some patients from each stratum. For this research study, we have a total of 21 strata. We are given that all strata have approximately the same size. So, will keep the same proportion of patients selected from each stratum in the random sample. So, we will get a stratified random sample.

4. Which do you think is the most correct method, especially given the hospital’s goals?

For the given scenario, the most correct method is stratified random sampling because this sampling techniques gives proper representativeness for each wing and also patients from each wing would be randomly selected. If we use simple random sampling, then the proportion of the patients from different wings would not be the same. Also, if we use the cluster sampling, then some wings do not get proper representativeness for this research study.