Question

A past survey of 1 comma 068 comma 000 students taking a standardized test revealed that 7.9​% of the students were planning on studying engineering in college. In a recent survey of 1 comma 476 comma 000 students taking the​ SAT, 9.2​% of the students were planning to study engineering. Construct a 95​% confidence interval for the difference between proportions p 1 minus p 2 by using the following inequality. Assume the samples are random and independent. left parenthesis ModifyingAbove p with caret 1 minus ModifyingAbove p with caret 2 right parenthesis minus z Subscript c Baseline StartRoot StartFraction ModifyingAbove p with caret 1 ModifyingAbove q with caret 1 Over n 1 EndFraction plus StartFraction ModifyingAbove p with caret 2 ModifyingAbove q with caret 2 Over n 2 EndFraction EndRoot less than p 1 minus p 2 less than left parenthesis ModifyingAbove p with caret 1 minus ModifyingAbove p with caret 2 right parenthesis plus z Subscript c Baseline StartRoot StartFraction ModifyingAbove p with caret 1 ModifyingAbove q with caret 1 Over n 1 EndFraction plus StartFraction ModifyingAbove p with caret 2 ModifyingAbove q with caret 2 Over n 2 EndFraction EndRoot The confidence interval is nothingless thanp 1 minus p 2less than nothing.

Answer 1

from above 95% Confidence interval =(-0.0137 <p1-p2<-0.0123)

*(please try -0.014 < p1-p2< -0.012 if requied with 3 decimals)