To estimate the most likely mean of the population from which the samples were taken, we can consider the means of the given samples. The sample means are as follows:
- 11.8
- 12.5
- 15.1
- 14.3
- 13.0
- 12.9
First, let's calculate the overall mean of the sample means:
\[ \text{Overall Mean} = \frac{(11.8 + 12.5 + 15.1 + 14.3 + 13.0 + 12.9)}{6} \]
Calculating the sum:
\[ 11.8 + 12.5 + 15.1 + 14.3 + 13.0 + 12.9 = 12.9 + 14.3 + 15.1 + 12.5 + 11.8 + 13.0 = 12.9 + 14.3 + 15.1 + 12.5 + 11.8 + 13.0 = 79.6 \]
Therefore,
\[ \text{Overall Mean} = \frac{79.6}{6} \approx 13.27 \]
Now, let's analyze the provided possible values for the population mean:
- 10.2
- 11.5
- 12.9
- 15.4
From the calculated overall mean (approximately 13.27), the value closest to this mean is 12.9. Therefore, 12.9 is the most likely value to represent the population mean of the underlying samples.