A biologist reports a confidence interval of (3, 2, 3, 8) when estimating the mean height in (in centimeters) of a sample of seedlings. The estimated margin of error is __________ , The sample mean is ________.
Add the two values together, then divide by 2 to get the mean:
3.2 + 3.8 = 7.0
Divide 7.0 by 2 = 3.5 = mean
Margin of error = .3
3.5 - .3 = 3.2
3.5 + .3 = 3.8
I hope this will help you with other problems of this type.
To find the estimated margin of error, we need to use the formula:
Margin of Error = (Upper Limit - Lower Limit) / 2
In this case, the upper limit is 8 and the lower limit is 2. Therefore,
Margin of Error = (8 - 2) / 2 = 6 / 2 = 3
So, the estimated margin of error is 3 centimeters.
To find the sample mean, we need to calculate the average of the confidence interval values:
Sample Mean = (3 + 2 + 3 + 8) / 4 = 16 / 4 = 4
So, the sample mean is 4 centimeters.
To determine the estimated margin of error and the sample mean, we need to understand the concept of a confidence interval.
A confidence interval is a range of values that gives us an estimate of the true population parameter. In this case, the biologist is estimating the mean height of a sample of seedlings.
The given confidence interval is (3, 2, 3, 8). It appears to have a typographical error since confidence intervals typically have two values, not four. For the purposes of answering your question, let's assume that the confidence interval is (3, 8).
The estimated margin of error can be determined by calculating half of the width of the confidence interval. The width of the confidence interval is calculated by subtracting the lower bound from the upper bound:
Width = Upper Bound - Lower Bound
= 8 - 3
= 5
Since the margin of error is the half width, we can calculate it as:
Margin of Error = Width / 2
= 5 / 2
= 2.5
So, the estimated margin of error is 2.5 centimeters.
To find the sample mean, we can take the average of the lower and upper bounds of the confidence interval:
Sample Mean = (Lower Bound + Upper Bound) / 2
= (3 + 8) / 2
= 11 / 2
= 5.5
Therefore, the sample mean is 5.5 centimeters.