The image you uploaded appears to be a statistical analysis regarding goalkeeping strategies (either staying in the center or diving) during penalties, specifically comparing the save and score percentages between the two strategies. Let's break it down:

1. Null and Alternative Hypotheses:

• Null Hypothesis (H₀): There is no significant difference between the save percentages of staying in the center and diving. The observed difference is due to random chance.
• Alternative Hypothesis (Hₐ): There is a significant difference in the save percentages between goalkeepers staying in the center and those who dive. One method is more effective than the other.

2. Test Statistic Calculation:

• You calculated a test statistic using the difference in observed percentages:
  $\text{Test Statistic} = 33.33\% - 13.43\% = 19.9\%$ or 0.199.
  This indicates the percentage difference in saves between staying in the center and diving.

3. Simulation Explanation:

• The simulation is run by preparing index cards to represent the outcomes based on the two strategies: "Stay" and "Dive".
  • For "Stay", you use 6 cards for "Stopped" and 12 for "Scored" (18 total).
  • For "Dive", you use 36 for "Stopped" and 232 for "Scored" (268 total).
  • After shuffling, you simulate 100 trials, keeping track of whether the outcome was "Stopped" or "Scored."
• A dotplot of the results helps visualize how the success percentages behave under random conditions.

4. Comparison to Random Chance:

• The comparison involves observing if the 19.9% difference (test statistic) could have arisen by random chance, according to the simulation. If the observed difference is large enough, it suggests that the save percentages differ significantly between strategies.

Would you like me to go into detail on any specific section or clarify any part of the analysis?

5 Follow-up Questions:

1. What significance level (e.g., 5%) are you using to determine whether the difference is statistically significant?
2. How many trials did you run in the simulation, and were the results consistent across those trials?
3. What were the simulated differences in the dotplot? Did they cluster around a particular value?
4. How does this analysis account for other variables (e.g., shooter’s skill)?
5. What would the next steps be if the null hypothesis is rejected?

Tip: When comparing proportions, consider using confidence intervals to determine the range of plausible values for the true difference in success rates.