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During the 2013-2014 NBA regular season, Lebron James attempted 306 3-point shots and made 116 of
them, for a 37.9% success rate. In the playoffs, he attempted 86 3-point shots and made 35 of them, for
a success rate of 40.7%. Does Lebron perform better in the playoffs, or is it possible that this difference
in the proportion of success could reasonably happen by random chance? Use the applet to run a
simulation with 100 trials. What number do I fill in the question mark box ?

To analyze whether LeBron James's performance in the playoffs represents an improvement or could happen by random chance, we need to simulate outcomes based on his observed regular season performance and compare it with the playoff performance.

Here's how you would approach this:

1. **Observed Regular Season Success Rate**: LeBron's success rate during the regular season was 37.9%.
2. **Simulate Playoff Successes**: Using the applet, we input a probability of success of 0.379 (LeBron's regular season percentage) and simulate 100 performances, each consisting of 86 attempts (the number of shots in the playoffs).
3. **Simulated Results Analysis**: We want to see if achieving or exceeding a 40.7% success rate (equivalent to 35 or more successful shots out of 86 attempts) could reasonably occur by chance.

**Steps to find the answer**:

1. Look at the dot plot created by the applet after 100 simulations.
2. Count the dots where the number of successful shots is **greater than or equal to 35** (which corresponds to the playoff success level of 40.7%).

The **question mark box** should be filled with the value **35**, as we're interested in the number of simulations that resulted in 35 or more successes to see if the playoff performance could be a product of random chance.

Would you like more details on interpreting these results, or have any questions on this process?

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**Related Questions**:
1. How does the observed difference in success rates between regular season and playoffs affect conclusions?
2. What does it mean statistically if only a few trials reach or exceed the playoff success rate?
3. How would increasing the number of trials (e.g., from 100 to 1000) affect the interpretation?
4. What are other possible statistical tests to verify LeBron’s performance difference?
5. How would this method change if we used data from multiple seasons?

**Tip**: Simulating with a higher number of trials can give a clearer view of whether the observed playoff performance is significant.

During the 2013-2014 NBA regular season, Lebron James attempted 306 3-point shots and made 116 of them, for a 37.9% success rate. In the playoffs, he attempted 86 3-point shots and made 35 of them, for a success rate of 40.7%. Does Lebron perform better in the playoffs, or is it possible that this difference in the proportion of success could reasonably happen by random chance? Use the applet to run a simulation with 100 trials. What number do I fill in the question mark box?

Analyze LeBron James's 3-point shooting performance from the 2013-2014 NBA season using probability and hypothesis testing. This problem simulates his success rate during regular season and playoff games to determine if the difference is statistically significant or due to random chance. Includes step-by-step instructions on running a simulation with 100 trials.

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