Question

a pharmaceutical company wants to conduct a survey of 30 individuals who have high cholesterol. the company has obtained a list from primary care physicians throughout the country of 5400 individuals who are known to have high cholesterol. design a sampling method to obtain the individuals in the sample. be sure to support the choice.

what sampling method(s) is/are valid? select all that apply

a. group the individuals by common primary care physician. for each group, assign all the individuals different numbers, and use a random number table to select an appropriate number of individuals.

b. select a hospital at random from a list of all of the country’s hospitals. survey individuals that pass by the front desk until there are responses from 30 individuals with high cholesterol.

c. group the individuals by common primary care physician. assign each physician a different number and use a random number table to select physicians until the total number of patients of all the selected physicians is at least 30

d. alphabetize the list of 5400 individuals by last name and select one of the first 180 individuals at random. starting from the selected individual, read down the list and select every 180th individual

Explanation:

• Option A: This is stratified random sampling (grouping by physician, then random selection within groups), which ensures representation across different physician patient groups and is valid.
• Option B: This is convenience sampling (surveying people at a hospital desk), which introduces bias as it only samples those visiting that specific hospital and is not valid.
• Option C: This is cluster sampling (treating physician patient lists as clusters, selecting clusters until sample size is met), which is valid as it uses random selection of clusters from the population.
• Option D: This is systematic random sampling (calculating sampling interval $\frac{5400}{30}=180$, then selecting every 180th individual after a random start), which is a valid probability sampling method.

Answer:

A. Group the individuals by common primary care physician. For each group, assign all the individuals different numbers, and use a random number table to select an appropriate number of individuals.
C. Group the individuals by common primary care physician. Assign each physician a different number and use a random number table to select physicians until the total number of patients of all the selected physicians is at least 30
D. Alphabetize the list of 5400 individuals by last name and select one of the first 180 individuals at random. Starting from the selected individual, read down the list and select every 180th individual