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

Solution Steps

The confidence interval for the mean of a single population with known variance at a 95.00% confidence level is calculated as follows:

\[ \bar{x} \pm z \frac{\sigma}{\sqrt{n}} = 50 \pm 1.96 \cdot \frac{5}{\sqrt{30}} = (48.21, 51.79) \]

Thus, the confidence interval is:

\[ \text{Confidence Interval} = (48.21, 51.79) \]

The point estimate of the population mean \( \mu \) is given by the average of the upper and lower confidence limits:

\[ \bar{x} = \frac{\text{(upper limit)} + \text{(lower limit)}}{2} = \frac{51.79 + 48.21}{2} = 50.0 \]

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

\[ \mu = \text{(upper limit)} + \text{(lower limit)} = 51.79 + 48.21 = 100.0 \]

This calculation is not valid in the context of confidence intervals.

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

\[ 2E = \text{(upper limit)} - \text{(lower limit)} = 51.79 - 48.21 = 3.58 \]

The margin of error \( E \) is calculated as half the difference between the upper and lower limits:

\[ E = \frac{\text{(upper limit)} - \text{(lower limit)}}{2} = \frac{51.79 - 48.21}{2} = 1.79 \]

Final Answer