Question

When can be inferred from two data sets that have normal distributions with a lot of overlap?

-The standard deviations are very similar between the data sets.
-The means of the data sets are very different from each other.
-It is very likely the data sets are significantly different from each other.
-It is unlikely the data sets are significantly different from each other.

Answer 1

When there is a lot of overlap between two data sets with normal distributions, it is unlikely that the data sets are significantly different from each other.

Step-by-step explanation:

When there is a lot of overlap between two data sets that have normal distributions, it can be difficult to make conclusive inferences. However, we can consider the following:

1. If the standard deviations are very similar between the data sets, it suggests that the spread of the data is similar.
2. If the means of the data sets are very different from each other, it indicates a significant difference in the central tendencies.
3. If the data sets are unlikely to be significantly different from each other, it means that the overlapping region is large enough to suggest similarity.

Therefore, based on these considerations, the correct answer is: It is unlikely the data sets are significantly different from each other.