Use the confidence interval to find the margin of error and the sample mean. \[ (0.278,0.380) \]

Step 1 ：The confidence interval is given by the formula: \(\bar{x} \pm E\), where \(\bar{x}\) is the sample mean and \(E\) is the margin of error.

Step 2 ：Given the confidence interval \((0.278, 0.380)\), we can find the sample mean \(\bar{x}\) by calculating the midpoint of the interval, and the margin of error \(E\) by calculating half the width of the interval.

Step 3 ：Calculate the sample mean: \(\bar{x} = \frac{0.278 + 0.380}{2} = 0.329\)

Step 4 ：Calculate the margin of error: \(E = \frac{0.380 - 0.278}{2} = 0.051\)

Step 5 ：Final Answer: The sample mean is \(\boxed{0.329}\) and the margin of error is \(\boxed{0.051}\)