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Should Matt (aka Spicy Curry) Wear a Shooting Sleeve to the

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by on 9 March 2018

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Transcript of Should Matt (aka Spicy Curry) Wear a Shooting Sleeve to the

Should Matt (aka Spicy Curry) Wear a Shooting Sleeve to the Next LSB Game?
The Background
As the rec league playoffs begin, Matt looks to gain an edge on the competition. Would wearing a shooting sleeve help Matt lead LSB to an unprecedented championship run?
Background 2
Popularized in the 2000's by AI, today it is commonly seen on stars such as Kyrie, Russel Westbrook, and LeBron. It thought to increase blood circulation and prevent muscle tightening.
The Question: Does wearing a shooting sleeve
significantly improve Matthew’s 3-point field goal % from the top of the key?

Definitions:
psleeve is the true proportion of made 3-pointers from the top of the top of the key for Matt while wearing the shooting sleeve
pno sleeve is the true proportion of made 3-pointers from the top of the key for Matt without wearing the shooting sleeve

Hypothesis:
H0: psleeve=pno sleeve OR psleeve-pno sleeve=0
Ha: psleeve>pno sleeve OR psleeve-pno sleeve>0

Data Collection
Data was collected at the Saline Rec center. I started by having Matt warm up for 10 minutes, to ensure that not being warmed up was not a confounding variable. I had Matt shoot 50 with the sleeve and 50 without it. I broke it down into 20 shot intervals, where the first 10 were either with or without the sleeve, and was determined by a coin toss. There was a 5 minute break every 20 shots to prevent fatigue. Matt used the same ball and shot from the top of the key for consistency.
Data Display
Interpretation
The pie charts and the
bar graph show us that Matt’s proportion of 3-pointers made is 4% greater with the shooting sleeve. Because Matt made a higher percentage of 3-pointer with the sleeves, as shown in the graphs, we have reason to doubt the null hypothesis that the 3-point percentage is the same. Although there is a difference in proportions (0.04), it is not that great of a difference, as shown in the graph, and these results could occur by random chance, so we should run a test to see the probability that obtaining a result this or more extreme if the null hypothesis is true.

State
Is there evidence that Matt shoots at a higher percentage from the top of the key with a shooting sleeve than without one?
H0: psleeve=pno sleeve OR psleeve-pno sleeve=0
Ha: psleeve>pno sleeve OR psleeve-pno sleeve>0
psleeve is the true proportion of made 3-pointers from the top of the top of the key for Matt while wearing the shooting sleeve
pno sleeve is the true proportion of made 3-pointers from the top of the key for Matt without wearing the shooting sleeve

Plan
Use a 2-proportion z-test if conditions allow.
Random- the two treatments are independent and randomly assigned via coin flip. After every 20 shots, the coin is flipped to determine if Matt will shoot with or without the sleeve for the first 10 shots.
Independence- we assume each shot is independent, and one shot does not affect another shot. We are not sampling without replacement, so we do not need to check the 10% rule.
Normality/large counts-
With Shooting Sleeve: n(p-hat)=50(0.64)=32>10; n(q-hat)=50(.36)=18>10 ⇒ therefore, the sampling distribution of the proportion of 3-pointers made with the shooting sleeve is approximately normal
Without shooting sleeve: n(p-hat)=50(.60)=30>10; n(q-hat)=50(.40)=20>10 ⇒ therefore, the sampling distribution of the proportion of 3-pointers made without the shooting sleeve is approximately normal

Do
Conclude
Because our p-value of 0.340 is significantly greater than our alpha value 0f 0.05, we fail to reject the null hypothesis, meaning we do not have statistically significant evidence that Matt wearin
g a shooting sleeve will increase his 3-point shooting percentage from the top of the key. Because our p-value is so high, it is likely that the difference in the 3-point percentages is due to random chance alone, in fact, there is a 0.340 probability of getting a difference in 3-point percentages this extreme or more extreme if it is true that shooting sleeves have no effect on 3-point shooting percentage. In conclusion, Matt wearing a shooting sleeve to the next basketball game will likely have no effect on his 3-point field goal percentage (from the top of the key).

Reflect
I had a great time working on this project. It was a pleasure to work with Rec basketball All Star and 3-point specialist Matt Eitzman. Arranging the procedure and collecting the data went without incident and were fairly straightforward. The hardest part of the experiment was finding a time when the rec center was not crowded in order to collect the data. Prior to collecting the actual data, Matt and I went to the rec center twice, only to find it was too crowded to effectively carry out the experiment. I was a bit disappointed in the fact that there was not statistically significant evidence to reject the null hypothesis. If I were to repeat this experiment, I would definitely consider raising n to 1000, and doing 500 shots with and without the sleeve, still taking breaks after every 20 shots. This would increase the power of the test, so if there is a difference in Matt’s 3-point shooting percentage from the top of the key with and without the shooting sleeve, the test would have a higher probability of detecting that. A potential drawback of this would be fatigue would certainly be a factor when taking that many shots, so data would probably have to be collected over a few days, which could be a possible confounding variable.
Another idea worth exploring would be doing a matched pairs design with this experiment, instead of just using one person. This would allow us to make inference about a broader population, instead of just an individual. Instead of using a 2-proportion z-test, we would used paired z procedures.

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