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 4% of 70%.

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 4% of 70%.

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.

jim_thompson5910 · Answer

I think the confidence level is 90% since 9/10 = 0.90 = 90%

The margin of error would be 4% with the point estimate being 70%

so the 90% confidence interval is (0.66, 0.74)

0.70 - 0.04 = 0.66
0.70 + 0.04 = 0.74

So basically the true mean is somewhere between 66% and 74%