To find the value of the test statistic and the corresponding p-value, we need to clarify the context of the hypothesis test being conducted. Given the data provided, the most likely test involves comparing average attendances across the three divisions (North, South, and West). In such a scenario, we would typically conduct a one-way ANOVA test to determine if there is a significant difference in the mean attendance across the divisions.

Steps:

1. Set up the Hypotheses:

   • Null Hypothesis ($H_0$): The mean attendance is the same across the three divisions.
   • Alternative Hypothesis ($H_1$): The mean attendance is different for at least one division.

2. Organize the data by division:

   • North Division Attendances: 8817, 8473, 9092, 6915, 7146, 5768
   • South Division Attendances: 4523, 6993, 6288, 4459
   • West Division Attendances: 7795, 8533, 9159, 8238

3. Conduct ANOVA Test: The ANOVA test will compare the variance between the group means (divisions) and the variance within the groups.

   Let's calculate the ANOVA test statistic and the corresponding p-value.

Formula for ANOVA F-statistic:

$F = \frac{\text{Mean Square Between Groups (MSB)}}{\text{Mean Square Within Groups (MSW)}}$

Where:

• $\text{MSB}$ is the variance between the group means.
• $\text{MSW}$ is the variance within the groups (based on the individual observations).

Let's compute these values.The value of the test statistic is $F = 6.97$ (rounded to two decimal places).

The corresponding p-value is $p = 0.011$ (rounded to three decimal places).

Since the p-value is less than 0.05, there is evidence to suggest that there is a significant difference in the average attendance between the divisions.

Would you like more details on this test, or help with interpretation?

Here are five related questions:

1. What is the next step after rejecting the null hypothesis in ANOVA?
2. How do you interpret the results of a post-hoc test like Tukey's HSD after ANOVA?
3. What are the assumptions underlying the one-way ANOVA test?
4. Can ANOVA handle more than one independent variable? If yes, how?
5. What other statistical tests can be used for comparing more than two groups?

Tip: If the p-value is low, it suggests strong evidence against the null hypothesis, meaning the group means are likely different.