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)

Answer 1

To find the difference between the mean heights of the two samples, we first need to calculate 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:**

\[
\text{Mean} = \frac{\text{Sum of heights}}{\text{Number of trees}}
\]

Calculating the sum of the heights for Sample 1:

\[
85.4 + 87.6 + 87.1 + 85.6 + 85.9 + 85.3 + 84.9 + 83.7 + 84.0 + 85.2 = 860.7
\]

Now, calculate the mean:

\[
\text{Mean}_1 = \frac{860.7}{10} = 86.07
\]

---

**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:**

Calculating the sum of the heights for Sample 2:

\[
87.1 + 88.0 + 84.2 + 85.3 + 86.5 + 84.2 + 83.2 + 84.1 + 85.2 + 87.3 = 860.1
\]

Now, calculate the mean:

\[
\text{Mean}_2 = \frac{860.1}{10} = 86.01
\]

---

**Calculating the Difference Between the Means:**

\[
\text{Difference} = \text{Mean}_1 - \text{Mean}_2 = 86.07 - 86.01 = 0.06
\]

Therefore, the difference between the mean heights of the trees of these two random samples is \( \boxed{0.06} \).