Question

To determine the average height of trees in a national forest, 10 trees are randomly selected. Their heights in feet are 85.4,87.6,87.1,85.6,85.9,85.3,84.9,83.7,84.0,and 85.2
. To ensure the accuracy of the data, another set of 10 trees is randomly selected. Their heights are 87.1,88.0,84.2,85.3,86.5,84.2,83.2,84.1,85.2,and 87.3
. What is the difference between the mean heights of the trees of these two random samples? Express your answer as a decimal. Do not round your answer.(1 point)
feet

Answer 1

To find the difference between the mean heights of the two samples of trees, we first need to calculate the mean height of each sample.

**For the first sample:**

Heights: 85.4, 87.6, 87.1, 85.6, 85.9, 85.3, 84.9, 83.7, 84.0, 85.2

1. **Calculate the sum of the heights:**

\[
85.4 + 87.6 + 87.1 + 85.6 + 85.9 + 85.3 + 84.9 + 83.7 + 84.0 + 85.2 = 867.7
\]

2. **Calculate the mean:**

\[
\text{Mean}_1 = \frac{867.7}{10} = 86.77
\]

**For the second sample:**

Heights: 87.1, 88.0, 84.2, 85.3, 86.5, 84.2, 83.2, 84.1, 85.2, 87.3

1. **Calculate the sum of the heights:**

\[
87.1 + 88.0 + 84.2 + 85.3 + 86.5 + 84.2 + 83.2 + 84.1 + 85.2 + 87.3 = 870.1
\]

2. **Calculate the mean:**

\[
\text{Mean}_2 = \frac{870.1}{10} = 87.01
\]

**Finally, calculate the difference between the means:**

\[
\text{Difference} = \text{Mean}_2 - \text{Mean}_1 = 87.01 - 86.77 = 0.24
\]

Thus, the difference between the mean heights of the trees of the two random samples is:

\[
\boxed{0.24}
\]