You are told that in a sample of size 225 the mean is 48.5 and the standard deviation is 1.8. The study is reported with 90% confidence level. Explain how to determine if 48.8 is within the confidence interval.

Answer:

To determine whether 48.8 is within the confidence interval, calculate the margin of error using ME = z* × s / √n. With z* = 1.645, s = 1.8, and n = 225, the margin of error is approximately 0.20. The confidence interval is 48.3 to 48.7, so 48.8 is not within the interval.