Final answer:
The correct answer to the student's question is 'a. Same; diverse,' indicating that various interpretations can be drawn from the same dataset. Differences in statistical results, like percentages, can arise due to sampling variability. Confidence intervals are used to determine the significance of differences in proportions.
Step-by-step explanation:
Different percentages can be reported from the same data set, with each percentage suggesting significantly diverse interpretations. The correct answer here is a. Same; diverse. This statement reflects the principles of data analysis, where how one presents and interprets data can lead to a variety of conclusions from the same numeric information. In the realm of statistics, small differences in percentages, such as the example provided (84 percent versus 86 percent), can be attributed to sampling variability. Sampling variability recognizes that different samples can produce different results, but as long as they're similar, they indicate consistency in the data rather than significant discrepancy.
When determining if differences in proportions are significant, researchers often look at confidence intervals. If the confidence intervals of different estimates overlap, it suggests that the differences might not be statistically significant. For proportions that do not overlap in their confidence intervals, this suggests a significant difference between the true proportions.
For instance, if researchers are comparing the percentage of all ethnicity C who would welcome persons of different ethnicities into their families and their confidence intervals overlap, it implies there is not a significant difference among these proportions. If the confidence intervals do not overlap, it indicates a significant difference in the true proportions regarding how welcoming the ethnicity is towards various other ethnicities.