A 96 % confidence interval for a mean was constructed. The confidence interval is as follows

6.1
±
3.5 .

What is the margin of error?

Recall: a confidence interval is computed using
𝑥
¯
±
𝐸
.

c07.p061.q025

Question

A 96 % confidence interval for a mean was constructed. The confidence interval is as follows

6.1
±
3.5 .

What is the margin of error?

Recall: a confidence interval is computed using    
𝑥
¯
±
𝐸
 .

c07.p061.q025

BlackTom AI · Accepted Answer

We start by restating what the provided interval shows: a mean is estimated with a confidence interval written as 6.1 ± 3.5. This format means the interval extends 3.5 units above and below the point estimate 6.1.

The margin of error (E) in a confidence interval is defined as the half-width of the interval. In general, a CI for a mean is written as x̄ ± E, where the interval limits are x̄ − E and x̄ + E.

From the given interval, the upper limit would be 6.1 + E and the lower limit would be 6.1 − E. The notation 6.1 ± 3.5 directly reveals that E = 3.5, since the width on either side of the center is 3.5.

Thus, the margin of error is the value that, when subtracted from and added to the sample mean, yields the lower and upper bounds of the confidence interval. Here, that value is 3.5.

A few related clarifications:
- The confidence level (96% in this case) determines how wide the interval tends to be across repeated samples, but it does not change the fact that E is the half-width of the reported interval.
- If you were given only the interval endpoints, you would compute E as half the distance between the endpoints: E = (Upper − Lower)/2. Here, 6.1 + 3.5 = 9.6 and 6.1 − 3.5 = 2.6, and indeed the half-width is (9.6 − 2.6)/2 = 3.5, matching the provided E.

Hence, the margin of error corresponding to this confidence interval is 3.5.

A 96 % confidence interval for a mean was constructed. The confidence interval is as follows 6.1 ± 3.5 . What is the margin of error? Recall: a confidence interval is computed using 𝑥 ¯ ± 𝐸 . c07.p061.q025简答题

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