2) A shoe manufacturer has developed a new running shoe that they claim will enable at least half of their wearers to run faster. A random sample of adults participated in a study in which they each ran a mile with their regular track shoe, and later ran a second mile with the new running shoe. The 95% confidence interval for the proportion of people who ran faster in the new running shoe was (0.46024 , 0.61976). a) Find the proportion of adults in the sample who ran faster in the new running shoe.

b) Find the number of people in the sample.

c) Does the confidence interval support the manufacturer's claim that the new running shoe will enable half of its wearers to run faster? Why or why not?