Question

ALGEBRA 2! HELP!!!

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.

Answer 1

The confidence interval is 90%, the reason being that nine times out of ten the confidence interval will contain the population mean.
5% of 75% is given by
\[\large 75\times\frac{5}{100}=3.75\ percent\]

Answer 2

Therefore the margin of error is 3.75%.

Answer 3

The confidence interval is (75 - 3.75, 75 + 3.75) = (71.25, 78.75)

Answer 4

Of course, if the statement "will have an average score within 5% of 75%" is taken to mean 'will have an average score within the interval 70% to 80%' the above results will need to be adjusted accordingly.