To determine if a valid prediction for the mean of the population can be made using these samples, we can consider the variability of the sample means.
The four sample means are:
- Sample 1: 7
- Sample 2: 4
- Sample 3: 5
- Sample 4: 8
The range of these sample means is from 4 to 8, and there is some variability among the samples.
Let's evaluate each of the provided options:
- "No, there are not enough samples." - It is true that four samples may not provide a robust estimate, but this is not the main issue here.
- "Yes, the sample means are all less than 10." - This statement is not inherently valid for predicting the population mean; it only states that the sample means are within a certain range.
- "Yes, the variation of the sample means is small." - The variation is somewhat small, but it may not be small enough to make a valid prediction confidently.
- "No, the variation of the sample means is too great." - Considering the limited number of samples and the range (4 to 8), there is enough variation to question the validity of making a population mean prediction.
Considering the variation and the limited number of samples, the most appropriate choice is:
No, the variation of the sample means is too great.