Questions: Which of the following calculations is NOT derived from the confidence interval? Choose the correct answer below. A. Difference between the limits, 2 E= (upper confidence limit) - (lower confidence limit) B. The population mean, μ= (upper confidence limit) + (lower confidence limit) C. The point estimate of μ, x̄= (upper confidence limit) + (lower confidence limit) / 2 D. The margin of error, E= (upper confidence limit) - (lower confidence limit) / 2

Which of the following calculations is NOT derived from the confidence interval?

Choose the correct answer below.
A. Difference between the limits, 2 E= (upper confidence limit) - (lower confidence limit)
B. The population mean, μ= (upper confidence limit) + (lower confidence limit)
C. The point estimate of μ, x̄= (upper confidence limit) + (lower confidence limit) / 2
D. The margin of error, E= (upper confidence limit) - (lower confidence limit) / 2
Transcript text: Which of the following calculations is NOT derived from the confidence interval? Choose the correct answer below. A. Difference between the limits, $2 E=$ (upper confidence limit) - (lower confidence limit) B. The population mean, $\mu=$ (upper confidence limit) + (lower confidence limit) C. The point estimate of $\mu, \bar{x}=\frac{\text { (upper confidence limit) }+ \text { (lower confidence limit) }}{2}$ D. The margin of error, $E=\frac{\text { (upper confidence limit) }- \text { (lower confidence limit) }}{2}$
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Solution

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Solution Steps

Step 1: Calculate the Difference Between the Limits

The difference between the upper and lower confidence limits is calculated as follows:

\[ 2E = \text{(upper confidence limit)} - \text{(lower confidence limit)} = 10 - 6 = 4 \]

Step 2: Calculate the Population Mean

The population mean is incorrectly calculated as the sum of the upper and lower confidence limits:

\[ \mu = \text{(upper confidence limit)} + \text{(lower confidence limit)} = 10 + 6 = 16 \]

Step 3: Calculate the Point Estimate of \(\mu\)

The point estimate of the population mean is the average of the upper and lower confidence limits:

\[ \bar{x} = \frac{\text{(upper confidence limit)} + \text{(lower confidence limit)}}{2} = \frac{10 + 6}{2} = 8.0 \]

Step 4: Calculate the Margin of Error

The margin of error is calculated as half the difference between the upper and lower confidence limits:

\[ E = \frac{\text{(upper confidence limit)} - \text{(lower confidence limit)}}{2} = \frac{10 - 6}{2} = 2.0 \]

Conclusion

From the calculations, we observe that:

  • Option A is derived from the confidence interval.
  • Option B, which states that the population mean is the sum of the upper and lower confidence limits, is incorrect.
  • Option C is derived from the confidence interval.
  • Option D is derived from the confidence interval.

Thus, the calculation that is NOT derived from the confidence interval is Option B.

Final Answer

\(\boxed{\text{B}}\)

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