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Use the confidence interval to find the margin of error and the sample mean

(12.0, 14.8)

User Avizzini
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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.

User Nknj
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