For question 26, the test statistic is derived by comparing the difference in winning percentages in two different conditions (home and away) to evaluate the significance of that difference.

Given:

• Home winning percentage = 0.625
• Away winning percentage = 0.475

To find the test statistic, calculate the difference between these percentages:

$\text{Test Statistic} = 0.625 - 0.475 = 0.15$

So, the test statistic for this scenario is 0.15.

For question 27, it asks about four common simulation methods to study the effect of random chance in repeated events. Common methods include:

1. Coin flipping – each flip represents a success or failure.
2. Dice rolling – each roll can simulate multiple outcomes with defined probabilities.
3. Random number generation – typically using software to generate numbers within a specified range.
4. Using a spinner – dividing a spinner into sections with probabilities matching the event's likelihood.

Would you like further explanations or have any questions about these methods or calculations?

Here are some related questions you might find helpful:

1. How is a test statistic used in hypothesis testing?
2. What is the purpose of a simulation in statistical analysis?
3. How do you choose a suitable simulation method for a particular study?
4. What are some limitations of using simulations to estimate probabilities?
5. How do you interpret the significance of a test statistic in a real-world context?

Tip: Always check the assumptions behind each simulation method to ensure they align with the event's actual probability structure.