To assess the effectiveness of a kindergarten-readiness program, 15 children from a random sample were each given a diagnostic a
ssessment before beginning the program and a follow-up assessment after completing the program. For each child, the difference in the score points between the two assessments was calculated and used to create the 95 percent confidence interval (20.1,23.9)(20.1,23.9). Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval?
A) For all children in the program, 95 percent of the children will have a mean difference in scores of between 20.1 points and 23.9 points.
B) There is a 0.95 probability that the mean difference in scores for all children in the sample is between 20.1 points and 23.9 points.
C) There is a 0.95 probability that the mean difference in scores for the children in the program is between 20.1 points and 23.9 points.
D) We are 95 percent confident that the mean difference in scores for all children in the program is between 20.1 points and 23.9 points.
E) We are 95 percent confident that the mean difference in scores for the children in the sample is between 20.1 points and 23.9 points.
D) We are 95 percent confident that the mean difference in scores for all children in the program is between 20.1 points and 23.9 points.
Step-by-step explanation:
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
95 percent confidence interval (20.1,23.9)
We are 95% sure that the population mean(that is, the mean for all children in the program) is in this interval. So the correct answer is given by option D.
