To determine which value is least likely to be the mean of the population from which the samples were taken, we can analyze the sample means provided:
- Sample 1: 15.2
- Sample 2: 17.1
- Sample 3: 16.9
- Sample 4: 12.2
- Sample 5: 18.0
- Sample 6: 16.3
- Sample 7: 17.4
Now, let's list the possible mean values from the options you provided:
- 12.2
- 15.3
- 16.4
- 17.5
Next, we can evaluate the values based on their relation to the sample means:
- 12.2 - This is the lowest sample mean noted (Sample 4), so it is plausible that the population mean could be around this value.
- 15.3 - This value is between the lowest sample mean of 12.2 and the highest sample mean of 18.0, making it a reasonable average.
- 16.4 - This value is also within the range of the sample means and appears to be a reasonable average.
- 17.5 - This is higher than several of the sample means and fairly close to the higher values in the sample means (17.1, 16.9, 17.4, 18.0). Thus, it could also be plausible.
However, the value of 12.2 is an actual sample mean, while the mean of 15.3 and 16.4 can be more closely related to the average of multiple samples. Whereas 17.5, while plausible, fits towards the higher end but not as consistently with the other means.
Thus, in conclusion, the value that is least likely to be the mean of the population from which these samples were taken is 12.2, as it is already represented as a sample mean. This makes it less likely to be the overall population mean compared to other provided values.