Anna Audler Stats 10: Section 3A UID: 304295761 TA: Luis Sosa Lab #3 Hot Hands Question 1: Kobe has a success rate of 43.6% for baskets made, as shown in the table below. This means that Kobe has a 0.436 probability of making a basket. Question 2: As shown in the distribution, Kobe has a typical (median) streak length of 0. The variability in the streak length is 0.973 from the mean (0.744). The distribution is right-skewed since the mean is to the right of the median. Question 3: Because each shot attempt is independent of the next, we can assume that the shooting probability will be the same after each shot. WE must replace the slips of paper after each drawing to make sure that the probability of making a shot is the same for every shot. So if we draw out a “miss”, we have to replace it otherwise there will be a higher probability of a “hit” than before. Kobe DataRowSummarybasketyesbasketno75 58133S1 = ( )countstreak0 1 2 3 4Kobe DataDot PlotQuestion 4: After adjusting the “Hot Hand Box” collection to match Kobe’s success rate, the collection now has 44 hits, which shows that a basketball player with the same success rate as Kobe would hit 44 out of 100 of his shots. Question 5: Fathom performs the simulation by random replacement, meaning the software randomly chooses an outcome, records it, and then replaces the outcome so the probability of getting either a “hit” or “miss” is the same. In this case, the 50th shot was a miss and had a streak of 0. Hot Hand BoxRowSummaryresultMissresultHit44 56100S1 = ( )countQuestion 6: The distribution of the simulation of the Hot Hand Box is right-skewed with a typical streak length of 0 and having a mean of 1.126. Question 7: Compared to the Kobe data (seen in Question 2), the simulated has a similar distribution: right-skewed and a typical value of 0. However, the mean for the simulated data is larger than Kobe’s mean; 1.128 > 0.744. In addition, the simulated data has a higher variation than Kobe’s: 1.342 > 0.973. Question 8: In my opinion, Kobe did not have “Hot Hands” during the 2009 Finals because his mean value for streaks was lower than the simulation, which used the same probability as Kobe’s 78 streaks. We would have expected Kobe’s mean value to be higher if he indeed had “hot hands.” In addition, each shot is independent of the next, so to say someone has “hot hands” is wrong because each shot does not influence the next. streak0 1 2 3 4 5 6 7Measures from Sample of Hot Hand BoxDot PlotKobe Datastreak0.743590.972824S1 = ( )meanS2 = ( )stdDevMeasures from Sample of Hot Hand Boxstreak1.128211.34221S1 = ( )meanS2 = ( )stdDevSummary Question: Topics covered in this lab include: shape of distribution, mean, standard deviation, probability, randomness, independence, replacement, and estimating probabilities via simulation. Each of these topics was covered in the Chapter 2 and 5 lectures and on Homework 4. Topics from chapter 5 that weren’t covered include: law of large numbers, certainty, complement rule, disjoint events, addition rule, multiplication rule, conditional probability, and Bayes
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