the company is concerned that a simple random sample of 2000 owners would include fewer than 12 owners of model d or fewer than 12 owners of model e. briefly describe a sampling method for randomly selecting 2000 owners that will ensure at least 12 owners will be selected for each of the 5 car models.
Models:
A:112338 b:96174 c:83241 d:3278 e:2323
To ensure that you select at least 12 owners for each of the five car models, you can use a stratified sampling method. Here's how you can do it:
1. Determine the proportion of owners for each car model based on the total population of owners. In this case, we have the following proportions:
- Model A: 112,338/1,000,354 ≈ 0.112
- Model B: 96,174/1,000,354 ≈ 0.096
- Model C: 83,241/1,000,354 ≈ 0.083
- Model D: 3,278/1,000,354 ≈ 0.003
- Model E: 2,323/1,000,354 ≈ 0.002
2. Multiply each proportion by the desired sample size of 2000 to get the target number of owners for each car model:
- Model A: 0.112 * 2000 = 224 owners
- Model B: 0.096 * 2000 = 192 owners
- Model C: 0.083 * 2000 = 166 owners
- Model D: 0.003 * 2000 = 6 owners
- Model E: 0.002 * 2000 = 4 owners
3. Randomly select owners from each car model group to reach or exceed the target number. You can do this by:
- Creating a list of owners for each car model.
- Assigning a unique identifier to each owner within their respective model group (e.g., 1 to 112,338 for Model A, 1 to 96,174 for Model B, and so on).
- Using a random number generator to select owners from each model group until you reach or exceed the target number of owners for each car model.
By following these steps, you can ensure that you randomly select 12 or more owners for each of the five car models in your sample of 2000 owners.