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# Express the Confidence Interval in the form of xbar +-E

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Express the Confidence Interval in the form of xbar +-E

Given Information:

Z interval: (291.67, 543.11)
xbar = 417.39
n=98

Choose correct confidence interval:

a) 417.39 +- 291.67
b) 417.39+-125.72

Why?

https://brainmass.com/statistics/confidence-interval/express-confidence-interval-form-xbar-30811

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Please see the attached Word document for solution and explanation.

Solution:

Recall the formula for finding a confidence interval:

You can see that when you calculate a confidence interval, you subtract an amount (your problem calls it E) from to get the left end point of the interval. Then you add that same amount to to get the right endpoint of the interval.

The problem tells you the left endpoint is 291.67, so the following must be true:

Since we know the value of , we can solve this for E.

So the correct answer is b) 417.39+-125.72

As a check, you can add this amount to and see if you get the right endpoint of the interval:

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