What are the confidence intervals for a dataset with a mean of 15 and EBM = 3.1? (2 marks)

1. Break Down the Problem

To find the confidence intervals for a dataset, we need to determine the lower and upper bounds using the provided mean and the Error Bound for the Mean (EBM).

2. Relevant Concepts

The confidence interval is calculated using the formula: $\text{Confidence Interval} = \text{Mean} \pm \text{EBM}$

Where:

• Mean = 15
• EBM = 3.1

3. Analysis and Detail

We will calculate the lower and upper limits of the confidence interval.

• Lower Limit: $\text{Lower Limit} = \text{Mean} - \text{EBM} = 15 - 3.1 = 11.9$

• Upper Limit: $\text{Upper Limit} = \text{Mean} + \text{EBM} = 15 + 3.1 = 18.1$

4. Verify and Summarize

We have calculated the lower and upper limits of the confidence interval based on the mean and EBM.

Final Answer

The confidence interval for the dataset is $[11.9, 18.1]$.