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?(1 point)
The mean height of the first set of 10 trees is (85.4 + 87.6 + 87.1 + 85.6 + 85.9 + 85.3 + 84.9 + 83.7 + 84.0 + 85.2)/10 = 85.28 feet.
The mean height of the second set of 10 trees is (87.1 + 88.0 + 84.2 + 85.3 + 86.5 + 84.2 + 83.2 + 84.1 + 85.2 + 87.3)/10 = 85.51 feet.
The difference between these two means is:
85.51 - 85.28 = 0.23 feet
Therefore, the difference between the mean heights of the two random samples is 0.23 feet.
Well, the first thing we need to do is calculate the mean height of each sample. Then we can find the difference between the two mean heights. Let's get to it!
For the first sample, the mean height is (85.4 + 87.6 + 87.1 + 85.6 + 85.9 + 85.3 + 84.9 + 83.7 + 84.0 + 85.2) / 10 = 859.7 / 10 = 85.97 feet.
For the second sample, the mean height is (87.1 + 88.0 + 84.2 + 85.3 + 86.5 + 84.2 + 83.2 + 84.1 + 85.2 + 87.3) / 10 = 855.2 / 10 = 85.52 feet.
Now, to find the difference between these two mean heights, we subtract them: 85.97 - 85.52 = 0.45 feet.
Therefore, the difference between the mean heights of the two random samples is 0.45 feet.
I hope my calculations didn't fall flat!
To find the difference between the mean heights of the two random samples, we need to calculate the means of each sample first.
First Sample Heights:
85.4, 87.6, 87.1, 85.6, 85.9, 85.3, 84.9, 83.7, 84.0, 85.2
Second Sample Heights:
87.1, 88.0, 84.2, 85.3, 86.5, 84.2, 83.2, 84.1, 85.2, 87.3
Step 1: Calculate the mean of the first sample
Sum of heights in the first sample = 85.4 + 87.6 + 87.1 + 85.6 + 85.9 + 85.3 + 84.9 + 83.7 + 84.0 + 85.2 = 854.7
Mean of the first sample = Sum of heights / Number of heights = 854.7 / 10 = 85.47
Step 2: Calculate the mean of the second sample
Sum of heights in the second sample = 87.1 + 88.0 + 84.2 + 85.3 + 86.5 + 84.2 + 83.2 + 84.1 + 85.2 + 87.3 = 854.2
Mean of the second sample = 854.2 / 10 = 85.42
Step 3: Find the difference between the means of the two samples
Difference = Mean of the first sample - Mean of the second sample
Difference = 85.47 - 85.42 = 0.05
Therefore, the difference between the mean heights of the two random samples is 0.05 feet.
To find the difference between the mean heights of the two random samples, we need to calculate the mean heights for each sample first.
For the first sample:
Sum of heights = 85.4 + 87.6 + 87.1 + 85.6 + 85.9 + 85.3 + 84.9 + 83.7 + 84.0 + 85.2 = 865.7
Mean height = Sum of heights / Number of trees = 865.7 / 10 = 86.57
For the second sample:
Sum of heights = 87.1 + 88.0 + 84.2 + 85.3 + 86.5 + 84.2 + 83.2 + 84.1 + 85.2 + 87.3 = 854.1
Mean height = Sum of heights / Number of trees = 854.1 / 10 = 85.41
Now, we can calculate the difference between the mean heights:
Difference = Mean height of first sample - Mean height of second sample
Difference = 86.57 - 85.41 = 1.16
Therefore, the difference between the mean heights of the two random samples is 1.16 feet.