a dairy farmer has black and brown milking cows. The farmer wants to know how much milk is produced on his farm daily. The farmer selects 15 black cows and 15 brown cows randomly by their tag numbers and logs the amount of milk produced each day for 1 week.
What type of sampling did the farmer use?
Is this a good sample, why or why not?
The farmer used a combination of stratified and random sampling. First, the farmer stratified the cows by color (black and brown), and then randomly selected 15 cows from each color group based on their tag numbers.
This sampling method can be considered a good sample because it ensures representation from both types of cows on the farm. By stratifying the cows by color, the farmer ensures that the sample is representative of the entire population, as it includes cows from both categories. Additionally, the random selection within each stratum helps to minimize any bias that could be introduced in the selection process.
The farmer used a method called simple random sampling. This means that each cow in the population (all the black and brown cows on the farm) had an equal chance of being selected for the sample.
As for whether it is a good sample, there are a few factors to consider.
Firstly, the size of the sample: The farmer selected 30 cows in total (15 black and 15 brown). While it may not represent the entire population, it can still provide a reasonable estimate of the average milk production on the farm.
Secondly, the randomness of the selection: By using tag numbers, the farmer ensured that the cows were chosen randomly from the population. This helps to avoid any bias or favoritism in the selection process.
Thirdly, the duration of the data collection: The farmer logged the milk production for a week. Having data for multiple days allows for a more accurate estimation of the daily milk production on the farm, taking into account any day-to-day variations.
Overall, this sampling method can provide a good approximation of the average milk production on the farm. However, it is important to note that the generalizability of the results may be limited to the specific week and the cows included in the sample.