Question 7.85

image 55. A telephone survey of 880 randomly selected drivers asked, “Recalling the last 10 traffic lights you drove through, how many of them were red when you entered the intersections?” Of the 880 respondents, 171 admitted that at least one light had been red.

  1. Give a 95% confidence interval for the proportion of all drivers who ran one or more of the last 10 red lights they came across.
  2. A practical problem with this survey is that people may not give truthful answers. What is the likely direction of the bias: Do you think more or fewer than 171 of the 880 respondents really ran a red light? Why?

55.

(a) The sample proportion who admit running a red light is . The approximate 95% confidence interval is calculated as follows:

The interval would be (0.167, 0.221).

A-20

(b) It is likely that more than 171 ran a red light, because some people are reluctant to admit illegal or antisocial acts.