Most traffic lights are set so that there is enough time for pedestrians to cross the road safely. A recent study indicates that a large number of elderly cannot get across the road in the usual 15 seconds allowed. To determine the average amount of time it takes senior citizens to cross the street, a study was taken of 25 seniors. On the average, it took them 19.5 seconds to cross the street, with a sample standard deviation of five seconds. Assume the time to cross the road has a normal distribution.
a). Set up the null and alternative hypotheses to see if the data show that it does indeed take seniors longer than 15 seconds to cross the street.
b). In terms of traffic flow, what are the implications of a Type I error?
c). What are the implications of a Type II error?
d). Find the value of the test statistic.
e). If alpha = 0.05, what is the rejection region?
f). What is your recommendation to the city?