1) On March 20, 2005, basketball player LeBron James of the Cleveland Cavaliers scored 56 points in a victory over the Toronto Raptors. During the game many fans suggested that LeBron had the hot hand. However, even though this was a truly amazing PERFORMANCE, it is possible that the outcomes of Lebron's shots were independent and he didn't have the hot hand. According to play-by-play data on espn.com, he made 17 shots in 34 attempts. a) Explain what it means for the outcomes of LeBron's shots to be independent. b) If we wanted to investigate if the LeBron's ABILITY to make a shot is greater following a made shot than following a missed shot, what hypotheses should we test? c) Describe a Type I and a Type II error in the context of this problem. d) One way to test these hypotheses is to consider Made the first |Missed the first Total each pair of shots during the Made the second 9 8 17 game. Here is a two-way Missed the second 8 8 16 table showing the results of Total 17 16 33 each pair of shots: How much better did the LeBron FERFORM after a made shot than after a missed shot? Show work