Identify the sampling method. Then identify any bias in each method. And show all work
A maintenance crew wants to estimate how many of 3000 air filters in an office building need replacing. The crew examines five filters chosen at random on each floor of the building.
@oobleck
Plse help
@mathhelper
sorry, not too up on statistical methods.
But surely by now you have managed to ferret out an answer...
The sampling method used in this scenario is called stratified random sampling. This method involves dividing the population (3000 air filters) into distinct groups or strata (in this case, each floor of the building), and then randomly selecting a certain number of samples (5 filters) from each stratum.
To identify any bias in each method, we need to consider if there is any systematic favoritism or deviation from randomness in the sample selection process. In this case, there are a few potential sources of bias:
1. Non-response bias: If the maintenance crew fails to examine all five randomly selected filters on each floor due to any reason (e.g., time constraints, lack of accessibility to certain areas), there may be a bias in the results towards those areas that were not examined.
2. Selection bias: If the maintenance crew does not truly select the filters randomly on each floor but instead deliberately or unconsciously favors certain filters (e.g., choosing filters that appear visibly dirty or damaged), this could introduce bias into the estimation.
3. Floor bias: There might be inherent differences between the floors in terms of air filter usage or conditions that could introduce bias into the estimation. For example, if some floors are closer to entrances or have higher traffic, the air filters on those floors may be dirtier on average, leading to overestimation of the number of filters needing replacement.
To mitigate these biases, it is important for the maintenance crew to follow a strict random selection process, ensuring that all floors are equally represented. Additionally, taking steps to minimize non-response bias, such as ensuring access to all areas and completing the examination of all selected filters, would help obtain a more accurate estimate.