To estimate the population mean using the samples provided, we can calculate the mean of each of the four samples and then find the overall mean of those means.
Let's calculate the means for each sample:
Sample 1: (4 + 5 + 2 + 4 + 3) / 5 = 18 / 5 = 3.6
Sample 2: (2 + 2 + 6 + 5 + 7) / 5 = 22 / 5 = 4.4
Sample 3: (4 + 6 + 3 + 4 + 1) / 5 = 18 / 5 = 3.6
Sample 4: (5 + 2 + 4 + 3 + 6) / 5 = 20 / 5 = 4.0
Now, we find the mean of these four sample means: (3.6 + 4.4 + 3.6 + 4.0) / 4 = 15.6 / 4 = 3.9
To find the range between which the population mean might lie, we can consider the lowest and highest sample means:
- The minimum sample mean is 3.6
- The maximum sample mean is 4.4
Thus, we can conclude that Ardem's actual population mean will lie between 3.6 and 4.4.
Among the provided options, the correct one is: 3.6 and 4.4