To calculate the difference between the mean heights of the two samples of trees, we first need to find the mean height for each sample.
Sample 1 heights: 85.4, 87.6, 87.1, 85.6, 85.9, 85.3, 84.9, 83.7, 84.0, 85.2
Calculating the mean for Sample 1: \[ \text{Mean}_1 = \frac{85.4 + 87.6 + 87.1 + 85.6 + 85.9 + 85.3 + 84.9 + 83.7 + 84.0 + 85.2}{10} \] \[ = \frac{864.7}{10} = 86.47 \]
Sample 2 heights: 87.1, 88.0, 84.2, 85.3, 86.5, 84.2, 83.2, 84.1, 85.2, 87.3
Calculating the mean for Sample 2: \[ \text{Mean}_2 = \frac{87.1 + 88.0 + 84.2 + 85.3 + 86.5 + 84.2 + 83.2 + 84.1 + 85.2 + 87.3}{10} \] \[ = \frac{864.1}{10} = 86.41 \]
Finding the difference between the means of the two samples: \[ \text{Difference} = \text{Mean}_1 - \text{Mean}_2 = 86.47 - 86.41 = 0.06 \]
Thus, the difference between the mean heights of the trees in the two random samples is 0.06 feet.