If you had a confidence interval for two groups of data that overlapped, what could you reasonably conclude?

A. That there was likely to be a difference in the variability of the two groups in the population.
B. That there was unlikely to be a difference between the means of the two groups in the population.
C. That there was unlikely to be a difference in the variability of the two groups in the population.
D. That there was likely to be a difference between the means of the two groups in the population.

Question

22-07-2024
Mathematics

Answered

If you had a confidence interval for two groups of data that overlapped, what could you reasonably conclude?

A. That there was likely to be a difference in the variability of the two groups in the population.
B. That there was unlikely to be a difference between the means of the two groups in the population.
C. That there was unlikely to be a difference in the variability of the two groups in the population.
D. That there was likely to be a difference between the means of the two groups in the population.

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-07-22T11:05:49-04:00

When evaluating confidence intervals for two groups, if the intervals overlap, we interpret this statistically to understand whether there might be a significant difference between the means of the groups. Let’s look at what overlapping confidence intervals might suggest step-by-step:

1. Confidence Interval Basics: A confidence interval provides a range of values, derived from sample data, that is believed to contain the true population parameter (such as the mean) with a certain level of confidence (often 95%).

2. Interpreting Overlapping Intervals: If the confidence intervals for two groups overlap, it implies that some of the values within those ranges are common to both groups.

3. Statistical Implication: Overlapping confidence intervals suggest that the difference between the two group means is not statistically significant. In simpler terms, the data does not provide strong evidence to suggest that the two groups have different means.

Given these interpretations, the reasonable conclusion from overlapping confidence intervals is:

- That there was unlikely to be a difference between the means of the two groups in the population.

In summary, when you observe overlapping confidence intervals for two groups, it indicates that we cannot confidently state that there is a significant difference between their means. Thus, the correct conclusion is that there was unlikely to be a difference between the means of the two groups in the population.