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

  2. Calculate the mean of Sample 1: \[ \text{Mean of Sample 1} = \frac{\text{Sum of Sample 1}}{10} = \frac{861.7}{10} = 86.17 \]

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 Sample 2 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 of Sample 2: \[ \text{Mean of Sample 2} = \frac{\text{Sum of Sample 2}}{10} = \frac{870.1}{10} = 87.01 \]

Difference Between the Means: Now, we find the difference between the mean heights of the two samples: \[ \text{Difference} = \text{Mean of Sample 2} - \text{Mean of Sample 1} = 87.01 - 86.17 = 0.84 \]

The difference between the mean heights of the two random samples is \( \boxed{0.84} \) feet.