To estimate the population mean from the sample, we first need to calculate the sample mean. The sample mean is calculated by summing all the values and dividing by the number of values.
Here are the sample responses you provided:
12, 9, 16, 9, 10, 11, 10, 14, 4, 2, 4, 0, 12, 1, 6
Now, let's calculate the sum of these values:
\[ 12 + 9 + 16 + 9 + 10 + 11 + 10 + 14 + 4 + 2 + 4 + 0 + 12 + 1 + 6 = 12 + 9 = 21\ 21 + 16 = 37\ 37 + 9 = 46\ 46 + 10 = 56\ 56 + 11 = 67\ 67 + 10 = 77\ 77 + 14 = 91\ 91 + 4 = 95\ 95 + 2 = 97\ 97 + 4 = 101\ 101 + 0 = 101\ 101 + 12 = 113\ 113 + 1 = 114\ 114 + 6 = 120 \]
So, the sum of the values is 120.
Next, we divide the sum by the number of responses (15) to get the sample mean:
\[ \text{Sample Mean} = \frac{\text{Sum}}{\text{Number of Responses}} = \frac{120}{15} = 8 \]
Thus, the estimated population mean based on the sample is 8.