Question

To study the long-term effects of preschool programs for poor children, researchers designed an experiment. They recruited $123$children who had never attended preschool from low-income families in Michigan. Researchers randomly assigned $62$of the children to attend preschool (paid for by the study budget) and the other 61 to serve as a control group who would not go to preschool. One response variable of interest was the need for social services as adults. In the past $10$years, $38$children in the preschool group and $49$in the control group have needed social services.

The Minitab output below gives a $95$% confidence interval for $p1-p2$. Interpret this interval in context. Then explain what additional information the confidence interval provides.

Short answer

From the given information, here, $0$does not lie in the computed confidence interval. Thus, it could be said that there is a difference in the two population proportions.

Step-by-step solution

Given Information

It is given in the question that,

Explanation

From the overhead output, the $95$% confidence interval for the difference in population proportions is $(0.0333680,0.347383)$. It hints that there is a $95$% chance that the dissimilarity in population proportion lies between $0.0333680$and $0.347383$

Here, $0$does not lie in the computed confidence interval. Thus, it could be said that there is a difference in the two population proportions.