What number do I plug in the stimulation 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.
a. Run the simulation and generate a dot plot using either proportions or the number of
successful shots to generate the dot plot. Take a screenshot and attach it here:
b. Use the counter at the bottom to count the number of dots that represent greater than his
performance.

To answer this question, we need to simulate whether the difference in LeBron's performance between the regular season and playoffs could reasonably happen by random chance. Here's how to approach the simulation and what numbers to plug in:

1. **Set up the null hypothesis**: The assumption that there is no real difference in LeBron’s 3-point performance between the regular season and the playoffs, and any observed difference is due to random chance.

2. **LeBron's overall success rate**: Combine both the regular season and playoff data to get a pooled proportion of successful shots.

- Regular season: 116 successful out of 306 attempts.
- Playoffs: 35 successful out of 86 attempts.

3. **Calculate the pooled proportion**:
   \[
   \text{Pooled proportion} = \frac{116 + 35}{306 + 86} = \frac{151}{392} \approx 0.385
   \]

   This pooled proportion (38.5%) represents LeBron's overall success rate across both the regular season and playoffs.

4. **Simulation setup**: 
   Using a simulation tool (like the applet mentioned in your problem), set the following:
   - Total number of trials: 100
   - Total number of attempts: 306 (for the regular season) and 86 (for the playoffs)
   - Success rate: 0.385 (the pooled proportion)
   
   In each trial, you will simulate random samples of 306 and 86 shots, assuming a 38.5% success rate, and calculate the difference in success rates for each trial.

5. **Generate the dot plot**:
   The dot plot will show the distribution of differences in proportions between the regular season and playoffs, based on random chance.

6. **Count dots greater than the observed difference**:
   - Calculate the actual observed difference: \(0.407 - 0.379 = 0.028\).
   - On the dot plot, count how many dots represent differences greater than 0.028 (which means LeBron performed significantly better in the playoffs).
   
7. **Conclusion**:
   If only a small number of dots exceed the observed difference, it suggests that the observed difference is unlikely to have occurred by chance, implying LeBron might indeed perform better in the playoffs. Conversely, if many dots exceed the observed difference, the difference could be attributed to random chance.

Would you like more details on any of these steps? Here are some relative questions for further practice:

1. How do you calculate the pooled proportion when combining two datasets?
2. What is the purpose of running a simulation in hypothesis testing?
3. How do you interpret the dot plot in a simulation?
4. Why is it important to account for random chance in performance analysis?
5. How would you calculate the confidence interval for LeBron's 3-point shooting success rate?

**Tip:** When running simulations, the larger the number of trials, the more reliable your conclusions will be.

What number do I plug in the simulation 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.

Analyze whether LeBron James performs better in the playoffs compared to the regular season by running a simulation with 100 trials. This problem involves calculating pooled proportions, simulating outcomes, and interpreting a dot plot. Perfect for students in Grades 10-12 studying hypothesis testing and simulation methods.

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