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 | 20               | 20        | 15        | 18               | 73 
sassafras | 24               | 16        | 16        | A=***            | 64 
Sum       | 44               | 36        | 31        | 26               | 137

Expected count
          | 1 (less than 15) | 2 (16-21) | 3 (22-26) | 4 (more than 26)
blackwood | 23.445           | B=***     | 16.518    | 13.854          
sassafras | 20.555           | 16.818    | 14.482    | 12.146          

chi-squared
          | 1 (less than 15) | 2 (16-21) | 3 (22-26) | 4 (more than 26)
blackwood | 0.506            | 0.035     | 0.14      | 1.241           
sassafras | 0.577            | 0.04      | 0.159     | 1.415           
A [integer]:	Answer 1 Question 1
B [use at least 3dp]:	Answer 2 Question 1


Let's work through these calculations:

### Finding the value of \( A \) (Observed Count Table)
In the observed count table, we know that the sum for the sassafras row should equal 64. Therefore, we can solve for \( A \) by subtracting the known values in the sassafras row from the total:

\[
A = 64 - (24 + 16 + 16) = 64 - 56 = 8
\]

So, \( A = 8 \).

### Finding the value of \( B \) (Expected Count Table)
The expected count \( B \) for blackwood in column 2 (16-21) can be calculated using the formula for expected frequency in contingency tables:

\[
\text{Expected Count}_{\text{(blackwood, 16-21)}} = \frac{(\text{Row Total for blackwood}) \times (\text{Column Total for 16-21})}{\text{Grand Total}}
\]

Plugging in the numbers:

\[
B = \frac{73 \times 36}{137} = \frac{2628}{137} \approx 19.175
\]

So, \( B \approx 19.175 \).

### Final Answers
1. \( A = 8 \)
2. \( B \approx 19.175 \)

Would you like a breakdown of these calculations, or do you have further questions?

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Here are 5 related questions to deepen your understanding:
1. How does one calculate expected counts in a contingency table for any given cell?
2. What does the chi-squared value signify in each cell of the table?
3. Why are expected values and chi-squared tests useful in studying associations between categorical variables?
4. How would this analysis change if there were more categories for age?
5. What additional information can be derived by examining residuals in the chi-squared test?

**Tip:** In contingency tables, double-check sums and totals after calculating any missing values to ensure accuracy.

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.

Solve a statistics problem involving contingency tables by finding missing values A and B, studying the association between age and species of felled trees. This example uses contingency tables, expected counts, and the chi-squared test, ideal for college-level statistics students.

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