Answers:
Margin of error = 1.4
Sample mean = 13.4
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Step-by-step explanation:
To find the margin of error, we subtract the endpoints and divide by 2.
(b-a)/2 = (14.8-12.0)/2 = 1.4 is the margin of error
The b-a portion calculates the width of the confidence interval. It's the distance from one endpoint to the other. Splitting that in half gives the "radius" so to speak of this interval.
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The sample mean is at the midpoint of those given confidence interval endpoints.
The midpoint formula will have us add up the values and divide by 2
(a+b)/2 = (12.0+14.8)/2 = 13.4 is the sample mean
The a+b portion is the same as b+a, meaning we could have written that formula as (b+a)/2 as indicated in the next section.
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Take note how similar each formula is:
- margin of error = (b-a)/2
- sample mean = (b+a)/2
The only difference is one has a minus sign and the other has a plus sign.