To find the best estimate of the mean of the population from the provided sample means, follow these steps:
1. Identify all the sample means provided in the table:
- Sample 1: 23.2
- Sample 2: 26.7
- Sample 3: 24.9
- Sample 4: 24.6
- Sample 5: 28.0
- Sample 6: 26.3
- Sample 7: 23.4
2. Add up all the sample means:
23.2 + 26.7 + 24.9 + 24.6 + 28.0 + 26.3 + 23.4
3. Calculate the total sum:
[tex]\( 23.2 + 26.7 + 24.9 + 24.6 + 28.0 + 26.3 + 23.4 = 177.1 \)[/tex]
4. Determine the number of samples, which is 7.
5. Compute the mean of these sample means by dividing the total sum by the number of samples:
[tex]\[
\text{Population Mean Estimate} = \frac{177.1}{7} = 25.3
\][/tex]
Therefore, the best estimate of the mean of the population is closest to 25.3, not 22.9 or 24.2. The given options do not match the calculated population mean, so neither 22.9 nor 24.2 are the best estimates. The correct estimate, based on the given data, is 25.3.
