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 5% of 75%.

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.

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 5% of 75%.

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.

kirbykirby · Answer

9 out of 10 means 90%, so in 9 out of 10 confidence intervals, you will find the true average score. 

The confidence interval and the margin of error are related in this way:
confidence interval: mean±(critical value)(standard error)
or as:
confidence interval: mean±(margin of error)

So the way they give you the information in the problem, 75 within 5% means $75 \pm 5=(75-5, 75+5)$
So the margin of error should be obvious now, and the confidence interval as well :o