Question

A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 6% of 80%.

Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation. (10 points)

Answer 1

"nine times out of ten" means we have 9/10 = 0.90 = 90% confidence interval.

The center of each interval is 0.80 as this is the mean test score. The margin of error is 0.06 from the statement "within 6% of...". Put another way, the teacher is basically saying that they are 90% confident to find a test score between 74% and 86%

This is because
0.8 - 0.06 = 0.74
0.8 + 0.06 = 0.86

So that's why the confidence interval is (0.74, 0.86)