Question

A basketball player with a 65% shooting percentage has just made 6 shots in a row. The announcer says this player “is hot tonight! She's in the zone!” Assume the player takes about 10 shots per game. Is it unusual for her to make 6 or more shots in a row during a game?

Model each component using equally likely random digits. Run ten trials

*I'm aware that I'll be using 10 two-digit numbers of 00-64 (indicates the player made the shot) and 65-99 (indicates the player didn't make the shot) but my question is how do I know when the trial outcome will equal a yes or no? I was looking at this question in the link and am not sure how they selected yes and no in the random number table. Also, how do I write out the random numbers should I be using a program? : https://www.chegg.com/homework-help/hot-hand-basketball-player-65-shooting-percentage-made-6-sho-chapter-10-problem-39e-solution-9780321986498-exc

Answer 1

.65 x 10 = 6.5(approx 7) per game, so 6 goals in a row is not unusual.

Random numbers: 48192 95308 72975 01191 29958 09275 89141 19558 50524 32041 02763 33701 66188 50226 35813 72951 11638 01876 93664 37001 42430 60322 34765 15757 53300 97392 98035 05228 68970 84432 04916 52949 78533 31666 62350 20584 56367 19701 60584 72042

The best ways we know to generate data that give a fair and accurate picture of the world rely on randomness.

Response variable: It will be categorical. If a trial results in 6 or more Y outcomes in a row, it is “yes.” Otherwise it is “no.”

description:-

A component consists of the player attempting one shot.

I will model each component using 2-digit random numbers between 00 and 99.

With this range I can accommodate her 65% shooting percentage exactly, with no discards

. Assignments: 00 - 64 = Y (shot made)

65 - 99 = N (shot missed)

Trial description: A trial will consist of repeatedly drawing 2-digit random numbers, and classifying them as Y or N according to the assignments given above. Trial ends when 10 random numbers have been drawn (which represents the 10 shots she attempts per game).

Response variable: It will be categorical. If a trial results in 6 or more Y outcomes in a row, it is “yes.” Otherwise it is “no.”

How I will estimate the required statistic: I will compute the % of “Y” values in my response variable.

Based on 3 trials, this player would make 6 shots in a row about 2/3 (or 67%) of the time