Im a great free-throw shooter. The Reasoning of a Statistical Test animates Example

Chapter 0, Problem 15.55

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Im a great free-throw shooter. The Reasoning of a Statistical Test animates Example 15.1. That example asks if a basketball players actualperformance gives evidence against the claim that he or she makes 80% of freethrows. The parameter in question is the percent p of free throws that the playerwill make if he or she shoots free throws forever. The population is all free throwsthe player will ever shoot. The null hypothesis is always the same, that the playermakes 80% of shots taken:H0 : p = 80%The applet does not do a formal statistical test. Instead, it allows you to ask theplayer to shoot until you are reasonably confident that the true percent of hits isor is not very close to 80%.David Madison/The Image Bank/Getty ImagesI claim that I make 80% of my free throws. To test my claim, we go to thegym and I shoot 20 free throws. Set the applet to take 20 shots. Check Show nullhypothesis so that my claim is visible in the graph.(a) Click Shoot. How many of the 20 shots did I make? Are you convincedthat I really make less than 80%?(b) If you are not convinced, click Shoot again for 20 more shots. Keep goinguntil either you are convinced that I dont make 80% of my shots or it appears thatmy true percent made is pretty close to 80%. How many shots did you watch meshoot? How many did I make? What did you conclude? Then click Show true %to reveal the truth. Was your conclusion correct?Comment: You see why statistical tests say how strong the evidence is againstsome claim. If I make only 10 of 40 shots, you are pretty sure I cant make 80% inthe long run. But even if I make exactly 80 of 100, my true long-term percent might be 78% or 81% instead of 80%. Its hard to be convinced that I makeexactly 80%.