Question

A confidence interval for a population mean has a margin of error of 3.5. a) Determine the length of the confidence interval. _____

b) If the sample mean is 51, obtain the confidence interval. Confidence interval: (___ , ___ ).

Answer 1

a) The length of the confidence interval is 7. b) The confidence interval is (47.5, 54.5).

Step-by-step explanation:

a) The length of the confidence interval is twice the margin of error. In this case, the margin of error is 3.5, so the length of the confidence interval is 2 * 3.5 = 7.

b) To obtain the confidence interval, we subtract and add the margin of error from the sample mean. The confidence interval is (51 - 3.5 , 51 + 3.5), which simplifies to (47.5, 54.5).