To assess whether LeBron James performs better in the playoffs or if the difference in his three-point shooting percentages could reasonably occur by random chance, we can use the SRiS applet for proportions.

Here are the steps to complete this analysis:

1. **Input the dataTo assess whether LeBron James performs better in the playoffs or if the difference in his three-point shooting percentages could reasonably occur by random chance, we can use the SRiS applet for proportions.

Here are the steps to complete this analysis:

1. **Input the **

   • Regular season: LeBron made 116 out of 306 attempts, which is 37.9%.
   • Playoffs: LeBron made 35 out of 86 attempts, which is 40.7%.

2. Simulate the differences:

   • Using the applet, input the number of attempts and success rates for both the regular season and the playoffs. Set the number of trials to 100.

3. Dot plot generation:

   • The applet will simulate 100 trials based on LeBron's performance and generate a dot plot of the differences in proportions between the regular season and playoffs. The plot will visually display whether the observed difference is unusual.

4. Count the dots:

   • After running the simulation, use the counter at the bottom of the dot plot to determine how many dots represent a performance greater than his actual playoff performance (40.7%). If the number of dots is low, it suggests that the observed improvement is unlikely due to random chance.

5. Interpretation:

   • If few dots represent a performance greater than the playoffs, it suggests that LeBron indeed performed better during the playoffs. Otherwise, if many dots exceed this threshold, the difference could reasonably be due to random variation.

You can run the simulation directly on the applet here to verify the results.

Do you need help running the applet, or would you like to ask any follow-up questions?

Follow-up questions:

1. What factors might affect a player's shooting percentage between regular season and playoffs?
2. How can we calculate confidence intervals for the difference in LeBron's performance?
3. What other statistical tests could be used to assess differences in performance?
4. How does the number of trials impact the reliability of the simulation results?
5. What assumptions does this simulation make about LeBron's shooting?

Tip:

Always double-check if external factors (like fatigue, defense intensity) could influence performance beyond randomness.