Final answer:
The discrepancy between the two researchers' findings on vaccination rates can be explained by sampling variability, which is an expected outcome of independent simple random sampling. The question involves understanding different sampling methods such as stratified, cluster, and simple random sampling.
Step-by-step explanation:
The question pertains to the subject of probability and statistics within Mathematics, specifically focusing on sample variation and sampling methods. When two researchers draw samples independently and find slightly different vaccination rates among children, a likely explanation for the discrepancy could be sampling variability. Sampling variability occurs because each sample drawn could have slightly different composition, despite both samples being random and representing the broader population well. Since the samples are both large enough and proportionately represent both successes (children up to date on vaccinations) and failures (children not up to date on vaccinations), the variation between 84 percent and 86 percent is an expected outcome of random sampling.
As for the types of sampling used in the given scenarios:
- Scenario a indicates stratified sampling, as the soccer coach divides the broader population into subgroups (strata) based on age and then selects players within each stratum.
- Scenario b utilizes cluster sampling, with the entire groups (human resource personnel from different companies) being included in the sample.
- Scenario c exemplifies simple random sampling, as an equal number of male and female teachers are randomly chosen without any stratification.