To estimate the mean of the population based on the given sample means, we need to calculate the average (mean) of the sample means provided. Here is a step-by-step breakdown:
1. List the sample means:
- 16.8
- 12.3
- 19.0
- 17.5
- 18.2
- 17.5
2. Calculate the sum of the sample means:
[tex]\[
16.8 + 12.3 + 19.0 + 17.5 + 18.2 + 17.5 = 101.3
\][/tex]
3. Count the number of sample means:
[tex]\[
\text{Number of sample means} = 6
\][/tex]
4. Calculate the average (mean) of the sample means by dividing the sum by the number of samples:
[tex]\[
\text{Population mean estimate} = \frac{101.3}{6} = 16.883333
\][/tex]
Next, we must compare this estimated population mean to the provided choices:
- 11.0
- 12.3
- 17.3
- 20.9
5. To identify the best estimate, find the choice that is closest to the calculated mean of 16.883333.
Let's calculate the absolute differences:
- [tex]\(|11.0 - 16.883333| = 5.883333\)[/tex]
- [tex]\(|12.3 - 16.883333| = 4.583333\)[/tex]
- [tex]\(|17.3 - 16.883333| = 0.416667\)[/tex]
- [tex]\(|20.9 - 16.883333| = 4.016667\)[/tex]
The smallest difference is for the value 17.3, which is closest to the estimated mean of 16.883333.
Therefore, the best estimate of the mean of the population based on the given sample means is [tex]\( \boxed{17.3} \)[/tex].
