In order to find the 95% confidence interval for the population mean, we need to use the sample mean and the margin of error. Here's the step-by-step process:
1. Identify the sample mean ( [tex]\(\bar{x}\)[/tex] ) and the margin of error (ME):
- Sample mean [tex]\(\bar{x} = 18.7\)[/tex]
- Margin of error [tex]\(ME = 5.9\)[/tex]
2. Calculate the lower and upper bounds of the confidence interval:
- The lower bound of the confidence interval is given by [tex]\(\bar{x} - ME\)[/tex].
- The upper bound of the confidence interval is given by [tex]\(\bar{x} + ME\)[/tex].
3. Substitute the values into the formulas:
- Lower bound = [tex]\(18.7 - 5.9\)[/tex]
- Upper bound = [tex]\(18.7 + 5.9\)[/tex]
4. Perform the calculations:
- Lower bound = [tex]\(18.7 - 5.9 = 12.8\)[/tex]
- Upper bound = [tex]\(18.7 + 5.9 = 24.6\)[/tex]
Therefore, the 95% confidence interval for the population mean is (12.8, 24.6).
Given the options, the correct representation of this confidence interval is:
[tex]\[ 18.7 \pm 5.9 \][/tex]
So, the correct answer is:
[tex]\[ 18.7 \pm 5.9 \][/tex]
