The International League of Triple-A minor league baseball consists of 14 teams organized into three divisions: North, South, and West. Suppose the following data show the average attendance for the 14 teams in the International League. Also shown are the teams' records; W denotes the number of games won, L denotes the number of games lost, and PCT is the proportion of games played that were won.

Team NameDivisionWLPCTAttendance

Buffalo Bisons

North

66

77

0.462

8817

Lehigh Valley IronPigs

North

55

89

0.382

8473

Pawtucket Red Sox

North

85

58

0.594

9092

Rochester Red Wings

North

74

70

0.514

6915

Scranton-Wilkes Barre Yankees

North

88

56

0.611

7146

Syracuse Chiefs

North

69

73

0.486

5768

Charlotte Knights

South

63

78

0.447

4523

Durham Bulls

South

74

70

0.514

6993

Norfolk Tides

South

64

78

0.451

6288

Richmond Braves

South

63

78

0.447

4459

Columbus Clippers

West

69

73

0.486

7795

Indianapolis Indians

West

68

76

0.472

8533

Louisville Bats

West

88

56

0.611

9159

Toledo Mud Hens

West

75

69

0.521

8238

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the *p*-value. (Round your answer to three decimal places.)

*p*-value =

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.

The International League of Triple-A minor league baseball consists of 14 teams organized into three divisions: North, South, and West. Suppose the following data show the average attendance for the 14 teams in the International League. Also shown are the teams' records; W denotes the number of games won, L denotes the number of games lost, and PCT is the proportion of games played that were won.
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)

Explore how to conduct a one-way ANOVA test to compare the average attendance across three baseball divisions using real data. Learn to calculate the F-statistic and p-value, including detailed steps for hypothesis testing and interpreting results. Suitable for undergraduate students studying statistics.

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