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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

1 answer

To find the difference between the mean heights of the two samples, we will first 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

  1. Calculate the sum of the heights: \[ 85.4 + 87.6 + 87.1 + 85.6 + 85.9 + 85.3 + 84.9 + 83.7 + 84.0 + 85.2 = 861.7 \]

  2. Divide the sum by the number of trees (10) to get the mean: \[ \text{Mean} = \frac{861.7}{10} = 86.17 \]

Sample 2 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: \[ 87.1 + 88.0 + 84.2 + 85.3 + 86.5 + 84.2 + 83.2 + 84.1 + 85.2 + 87.3 = 864.1 \]

  2. Divide the sum by the number of trees (10) to get the mean: \[ \text{Mean} = \frac{864.1}{10} = 86.41 \]

Difference between the means: Now we calculate the difference in the means of the two samples: \[ \text{Difference} = 86.41 - 86.17 = 0.24 \]

Thus, the difference between the mean heights of the trees from the two random samples is: \[ \boxed{0.24} \text{ feet} \]