AP Stats 1 Question

Question

Students at a local high school were randomly selected to participate in a math fluency program. The program is designed to increase their math fluency. A total of 12 students each took a pretest before the program and a posttest after the program. The mean of the differences in the posttest and pretest scores is 13. The administration decided that all students in the school would participate in the program next school year. Let µD denote the mean difference in the student scores. The 95 percent confidence interval estimate of the mean difference for all students is (8, 18). What is an appropriate interpretation of the confidence interval?

For any µ_D, the sample result is quite likely. 

For any µ_D with 8 < µ_D < 18, the sample result is quite likely. 

µ_D is positive, with a probability of 0.95. 

µ_D is negative, with a probability of 0.95. 

µ_D is between 8 and 18.

Answer 1

A 95% percent CI contains the plausible values of the population parameter with 95% confidence.

If 95% CI for mud is between 8 and 18, then we are 95% confident that the true value of mud is between 8 and 18 and thus we are 95% confident it is positive.