To estimate the mean of the population based on the seven sample means provided, we can calculate the overall mean (average) of these sample means. Here's how you can do it:
- Add all the sample means together.
- Divide by the total number of samples (which is 7 in this case).
Calculating the total:
\[ 23.2 + 26.7 + 24.9 + 24.6 + 28.0 + 26.3 + 23.4 = 177.1 \]
Now, divide by the number of samples (7):
\[ \text{Mean} = \frac{177.1}{7} \approx 25.3 \]
Now, comparing this calculated mean against the options provided:
- 22.9
- 24.2
- 28.2
- 29.1
The best estimate of the mean of the population from the options given is 24.2, as it is the closest to our calculated mean of approximately 25.3. However, it's important to note that the calculated mean is not one of the options.
Since 24.2 is the closest estimate to the mean calculated, it would be the best choice among the options provided.