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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 $95$% con铿乨ence interval for $p1-p2$. Interpret this interval in context. Then explain what additional information the con铿乨ence interval provides.

Step by step solution

01

Given Information

It is given in the question that,

02

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.

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