
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 | 22                   | 28                | 34                 |
Expected Count | B=***                | 11.3              | 56.5               |
chi squared    | 10.132               | 24.681            | C=***              |
               4 (more that 100,001) | Total 
Observed Count A=***                 | 113   
Expected Count 33.9                  | 113   
chi squared    0.708                 | 44.481
A [integer]:	Answer 1 Question 2
29
B [use at least 3dp]:

To complete the table, we need to calculate the following values:

1. **A (Observed Count for the category "4 - more than 100,001 followers")**
   
   To find this, we can use the total observed count (113) minus the sum of the observed counts for categories 1, 2, and 3.

   \[
   A = 113 - (22 + 28 + 34) = 113 - 84 = 29
   \]

   So, **A = 29**.

2. **B (Expected Count for the category "1 - less than 10,000 followers")**
   
   The expected count is calculated using the total expected count of 113 and the percentage for each category. The percentage for category 1 is 10%. Therefore, we can calculate:

   \[
   B = \frac{10}{100} \times 113 = 0.1 \times 113 = 11.3
   \]

   So, **B = 11.3** (this value is already provided in the table).

3. **C (Chi-squared value for category "3 - 50,001 to 100,000 followers")**
   
   The chi-squared statistic is calculated using the formula:

   \[
   \chi^2 = \frac{(Observed - Expected)^2}{Expected}
   \]

   For category 3:

   \[
   C = \frac{(34 - 56.5)^2}{56.5} = \frac{(-22.5)^2}{56.5} = \frac{506.25}{56.5} \approx 8.961
   \]

   So, **C ≈ 8.961**.

### Updated Table

|                                | 1 (less than 10,000) | 2 (10,001-50,000) | 3 (50,001-100,000) | 4 (more than 100,001) | Total |
|--------------------------------|----------------------|-------------------|--------------------|-----------------------|-------|
| **Observed Count**             | 22                   | 28                | 34                 | 29                    | 113   |
| **Expected Count**             | 11.3                 | 11.3              | 56.5               | 33.9                  | 113   |
| **Chi-squared**                | 10.132               | 24.681            | 8.961              | 0.708                 | 44.481|

Would you like more details or have any other questions?

---

Here are five questions that build on this topic:
1. How does the chi-squared statistic help determine the goodness of fit in this problem?
2. What is the null hypothesis in this chi-squared test?
3. How do we calculate degrees of freedom for a chi-squared test in this context?
4. How does changing the observed counts affect the chi-squared value?
5. Why is it important to compare observed and expected counts in statistical analysis?

**Tip:** The chi-squared test is sensitive to sample size, so a larger sample can make small differences statistically significant.

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 than 10,000) | 2 (10,001-50,000) | 3 (50,001-100,000) |
Percentage | 10 | 10 | 50 |

the number of followers of teams 4 (more than 100,001)
Percentage 30
Please complete the following table calculating the values of A, B and C.

| | 1 (less than 10,000) | 2 (10,001-50,000) | 3 (50,001-100,000) |
| Observed Count | 22 | 28 | 34 |
| Expected Count | B=*** | 11.3 | 56.5 |
| chi squared | 10.132 | 24.681 | C=*** |

4 (more than 100,001) | Total 
Observed Count A=*** | 113
Expected Count 33.9 | 113
chi squared 0.708 | 44.481

Explore how to use the chi-squared test to investigate the distribution of followers among teams in major international competitions. This problem covers calculating expected counts, observed counts, and chi-squared values for data analysis. Suitable for Grades 11-12.

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