**Research question:** We wish to investigate whether the number of followers of teams playing in major international team sporting competitions is distributed according to the table below.


the number of followers of teams | 1 (less that 10,000) | 2 (10,001-50,000) | 3 (50,001-100,000) |
Percentage                       |                   10 |                10 |                 50 |
                                                      
the number of followers of teams 4 (more that 100,001)
`Percentage                                          30`

Please complete the following table calculating the values of A, B and C.

               | 1 (less that 10,000) | 2 (10,001-50,000) | 3 (50,001-100,000) |
Observed Count | 28                   | A=***             | 23                 |
Expected Count | 10                   | 10                | B=***              |
chi squared    | C=***                | 16.9              | 14.58              |
               4 (more that 100,001) | Total 
Observed Count 26                    | 100   
Expected Count 30                    | 100   
`chi squared    0.533                 | 64.413`

To complete the table and determine the values of \( A \), \( B \), and \( C \), let’s proceed as follows:

### Step 1: Calculate \( A \) (Observed Count for Category 2)

The total Observed Count across all categories is given as 100. The observed counts for Categories 1, 3, and 4 are 28, 23, and 26, respectively. Since the sum of all Observed Counts must equal 100, we can set up the following equation:

\[
28 + A + 23 + 26 = 100
\]

Solving for \( A \):

\[
A = 100 - (28 + 23 + 26) = 100 - 77 = 23
\]

So, \( A = 23 \).

### Step 2: Calculate \( B \) (Expected Count for Category 3)

The total Expected Count across all categories is also given as 100. Since the expected percentage for Category 3 is 50%, we can calculate \( B \) as:

\[
B = 0.50 \times 100 = 50
\]

So, \( B = 50 \).

### Step 3: Calculate \( C \) (Chi-Squared Value for Category 1)

To find the chi-squared value \( C \) for Category 1, we use the chi-squared formula:

\[
\chi^2 = \frac{{(O - E)^2}}{E}
\]

where:
- \( O \) is the observed count,
- \( E \) is the expected count.

For Category 1:
- \( O = 28 \),
- \( E = 10 \).

Calculating \( C \):

\[
C = \frac{{(28 - 10)^2}}{10} = \frac{{18^2}}{10} = \frac{324}{10} = 32.4
\]

So, \( C = 32.4 \).

### Completed Table:

|                              | 1 (less than 10,000) | 2 (10,001-50,000) | 3 (50,001-100,000) | 4 (more than 100,001) | Total |
|------------------------------|----------------------|--------------------|---------------------|------------------------|-------|
| **Observed Count**           | 28                  | 23                | 23                 | 26                     | 100   |
| **Expected Count**           | 10                  | 10                | 50                 | 30                     | 100   |
| **Chi-Squared**              | 32.4                | 16.9              | 14.58              | 0.533                  | 64.413|

Would you like further clarification on any part of the solution?

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Here are five related questions to expand understanding:
1. How is the chi-squared test used to determine if a dataset fits an expected distribution?
2. What does the total chi-squared value indicate about the data's fit to the expected distribution?
3. How do degrees of freedom affect the interpretation of chi-squared results?
4. When should we consider an adjustment in expected values in real-world applications?
5. What are some common pitfalls when calculating chi-squared values?

**Tip:** Always check the degrees of freedom for your chi-squared test as it impacts the threshold for statistical significance.

We wish to investigate whether the number of followers of teams playing in major international team sporting competitions is distributed according to the table provided. The task involves calculating the values of A, B, and C in a table of observed and expected counts, as well as chi-squared values for each category.

Explore how to calculate chi-squared values to determine if the follower distribution of teams in international competitions matches expected percentages. This solution includes calculating observed and expected counts and applying the chi-squared formula. Suitable for college-level statistics students.

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