Problem 3) A random digit dialing telephone survey of 880drivers asked, “Recalling the intersections on your most recentdrive to work or school , were any of traffic lights red when youentered the intersections, i.e. did you run any red lights?†Of the880 respondents, 171 admitted that yes, at least one light had beenred.
a) What is the response variable? Is it categorical orquantitative?
b) Show that the normal approximation for p̂ is valid byverifying the three conditions. Include the arithmetic. (Rememberthat when we “assumed†that we knew π, we used nπ ≥ 10. Incontrast, this problem is reality where we do not know π: we aretrying to estimate π with a confidence interval. So, we use ?̂toestimate π in checking the condition.)
c) Estimate the population proportion of drivers who ran a redlight on the way to work or school with a 95 percent confidenceinterval. (Round the standard deviation to 2 nonzero decimals. Forexample, if you calculate ??Ì‚ to be 0.01234, round to 0.012.)
d) Interpret the confidence interval with a statement in thecontext of the problem.
