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 find the margin of error, multiply the z-score by the standard deviation, then divide by the square root of the sample size. The z*-score for a 90% confidence level is 1.645. The margin of error is 0.20. The confidence interval is 48.3 to 48.7. 48.8 is not within the confidence interval.