2. How do you decide when someone has gotten better at something when there is natural variability in their performance (e.g., how long it takes to swim a lap, how strong someone is in the gym, etc)? Suppose your friend's onerep max for bench press (the most weight that can be pushed in a single trial) is normally distributed with unknown mean and standard deviation of 6 pounds. Last year, you know the mean was 162 pounds, but your friend claims to be stronger now. a. Complete the PH of PHANTOM. b. Your friend proposes a test to decide between the hypotheses: They will perform a one-rep max and you'll use this to determine which hypothesis to support moving forward. If your friend bench-presses 180 pounds, what is the probability of seeing this event or something more extreme assuming the null hypothesis is true? [WISE, VIZ, Tables not tech] c. What conclusion should you draw for part b if a strange event in your mind is something that happens only 1 in a 100 times (or less often)? d. Another approach to testing your friend's claim is to have them perform 4 one-rep maxes (on different days) and use the average of the values to decide which hypothesis to believe. If your friend's results are 180, 160, 170, and 164, nd the average. Then, assuming the null hypothesis is true, state the distribution (shape, center, spread) the average follows, and calculate the probability of getting the observed average or something more extreme. [Tech not tables] e. What conclusion should you draw for part d if a strange event in your mind is something that happens only 1 in a 100 times (or less often)