Research question: we are interested in studying the association between the age of the felled tree and wood species in the population under consideration.
Please complete the following tables, calculating the values of A and B.

Observed count
          | 1 (less than 15) | 2 (16-21) | 3 (22-26) | 4 (more than 26) | Sum
blackwood | A=***            | 15        | 17        | 18               | 72 
sassafras | 13               | 19        | 13        | 7                | 52 
Sum       | 35               | 34        | 30        | 25               | 124

Expected count
          | 1 (less than 15) | 2 (16-21) | 3 (22-26) | 4 (more than 26)
blackwood | 20.323           | B=***     | 17.419    | 14.516          
sassafras | 14.677           | 14.258    | 12.581    | 10.484          

chi-squared
          | 1 (less than 15) | 2 (16-21) | 3 (22-26) | 4 (more than 26)
blackwood | 0.138            | 1.139     | 0.01      | 0.836           
sassafras | 0.192            | 1.577     | 0.014     | 1.158           
A [integer]:	Answer 1 Question 2
22
B [use at least 3dp]:

To find \( A \) and \( B \), let's follow these steps:

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

Since the total observed count for blackwood is 72, we can use this information to find \( A \).

1. Sum of the observed counts for blackwood in all categories:
   \[
   A + 15 + 17 + 18 = 72
   \]
2. Solving for \( A \):
   \[
   A = 72 - (15 + 17 + 18) = 72 - 50 = 22
   \]

Thus, \( A = 22 \).

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

The expected count in each cell is calculated by the formula:
\[
\text{Expected Count} = \frac{(\text{Row Total}) \times (\text{Column Total})}{\text{Grand Total}}
\]

For \( B \), the expected count for blackwood in category 2:
1. Row total for blackwood = 72
2. Column total for category 2 = 34
3. Grand total = 124

Then,
\[
B = \frac{72 \times 34}{124} = \frac{2448}{124} = 19.742
\]

Thus, \( B = 19.742 \) (rounded to three decimal places).

### Final Answer:
- **A** (Observed Count for Blackwood in Category 1): \( 22 \)
- **B** (Expected Count for Blackwood in Category 2): \( 19.742 \)

Research question: we are interested in studying the association between the age of the felled tree and wood species in the population under consideration. Please complete the following tables, calculating the values of A and B.

Observed count
          | 1 (less than 15) | 2 (16-21) | 3 (22-26) | 4 (more than 26) | Sum
blackwood | A=***            | 15        | 17        | 18               | 72 
sassafras | 13               | 19        | 13        | 7                | 52 
Sum       | 35               | 34        | 30        | 25               | 124

Expected count
          | 1 (less than 15) | 2 (16-21) | 3 (22-26) | 4 (more than 26)
blackwood | 20.323           | B=***     | 17.419    | 14.516          
sassafras | 14.677           | 14.258    | 12.581    | 10.484          

chi-squared
          | 1 (less than 15) | 2 (16-21) | 3 (22-26) | 4 (more than 26)
blackwood | 0.138            | 1.139     | 0.01      | 0.836           
sassafras | 0.192            | 1.577     | 0.014     | 1.158

This problem involves calculating the observed and expected counts for different categories of tree age and wood species using the chi-square test. Learn how to determine the values of A and B, as well as interpret the chi-squared results for statistical analysis. Suitable for students in Grades 11-12.

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