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)

Question

_ feet

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:

\[ \text{Mean}_1 = \frac{(85.4 + 87.6 + 87.1 + 85.6 + 85.9 + 85.3 + 84.9 + 83.7 + 84.0 + 85.2)}{10} \]

Summing the heights:

\[ 85.4 + 87.6 + 87.1 + 85.6 + 85.9 + 85.3 + 84.9 + 83.7 + 84.0 + 85.2 = 868.7 \]

Now, calculate the mean:

\[ \text{Mean}_1 = \frac{868.7}{10} = 86.87 \]

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:

\[ \text{Mean}_2 = \frac{(87.1 + 88.0 + 84.2 + 85.3 + 86.5 + 84.2 + 83.2 + 84.1 + 85.2 + 87.3)}{10} \]

Summing the heights:

\[ 87.1 + 88.0 + 84.2 + 85.3 + 86.5 + 84.2 + 83.2 + 84.1 + 85.2 + 87.3 = 866.1 \]

Now, calculate the mean:

\[ \text{Mean}_2 = \frac{866.1}{10} = 86.61 \]

Finding the difference between the two means:

\[ \text{Difference} = \text{Mean}_1 - \text{Mean}_2 = 86.87 - 86.61 = 0.26 \]

The difference between the mean heights of the trees from the two samples is

\[ \boxed{0.26} \text{ feet.} \]