To estimate the range of possible values for the population mean based on a sample mean, we need to consider the margin of error which allows us to establish a confidence interval around the sample mean.
Given:
- The sample mean is 94.
- The margin of error around this sample mean is 5.
To find the range of possible values (which is the confidence interval) for the population mean, we'll calculate:
1. Lower Bound: Subtract the margin of error from the sample mean.
[tex]\[
\text{Lower Bound} = 94 - 5 = 89
\][/tex]
2. Upper Bound: Add the margin of error to the sample mean.
[tex]\[
\text{Upper Bound} = 94 + 5 = 99
\][/tex]
Therefore, the range of possible values that best describes an estimate for the population mean is from 89 to 99.
So, the interval range for the population mean is 89 to 99, while the sample mean is 94.
