Answer :
Final Answer:
The confidence interval (-28, 277.4) can be expressed in the form of "Point Estimate ± Margin of Error" as [tex]\(124.7 \pm 152.4\).[/tex]
Explanation:
A confidence interval is a range of values that estimates the true value of a parameter with a certain level of confidence. In this case, the given confidence interval is (-28, 277.4), which represents the range of possible values for a parameter.
To express this confidence interval in the form of "Point Estimate ± Margin of Error," we first need to find the point estimate, which is the midpoint of the interval. The point estimate is calculated as the average of the upper and lower bounds:
[tex]\[ \text{Point Estimate} = \frac{-28 + 277.4}{2} = 124.7 \][/tex]
Next, we find the margin of error (ME), which is half of the interval width:
[tex]\[ \text{Margin of Error (ME)} = \frac{277.4 - (-28)}{2} = 152.4 \][/tex]
Finally, we can express the confidence interval as [tex]\(124.7 \pm 152.4\)[/tex], which indicates that we are 95% confident that the true parameter value falls within the range of 124.7 ± 152.4.
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