To solve this, we'll need to use the given percentages and observed counts to compute the missing values $A$, $B$, and $C$. The steps involve calculating the expected count, observed count, and chi-squared statistic for each category.

Step 1: Calculate A (Observed Count for category 3: 22-26)

We know the total observed count is 105. Therefore, using the observed counts for other categories, we can calculate $A$.

$A = 105 - (33 + 26 + 25) = 105 - 84 = 21$

Step 2: Calculate B (Expected Count for category 1: less than 15)

The expected count for each category is based on the percentage provided in the table. For category 1, the percentage is 10%. So, the expected count for category 1 is:

$B = 10\% \text{ of } 105 = 0.10 \times 105 = 10.5$

Step 3: Calculate C (Chi-squared value for category 4: more than 26)

The chi-squared statistic for each category is calculated using the formula:

$\chi^2 = \frac{(O - E)^2}{E}$ where $O$ is the observed count and $E$ is the expected count.

For category 4 (more than 26), we know:

• $O = 25$
• $E = 10.5$

Substituting these values into the formula:

$C = \frac{(25 - 10.5)^2}{10.5} = \frac{(14.5)^2}{10.5} = \frac{210.25}{10.5} = 20.024$

Final Table

Age of tree	1 (less than 15)	2 (16-21)	3 (22-26)	4 (more than 26)	Total
Observed Count	33	26	21	25	105
Expected Count	10.5	63	21	10.5	105
Chi-squared	48.214	21.73	0	20.024	89.968

Answers:

• $A = 21$
• $B = 10.5$ (3 decimal places)
• $C = 20.024$

Would you like further details or clarifications?

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Related Questions:

1. How is the chi-squared statistic used in hypothesis testing?
2. What assumptions are made when using the chi-squared test?
3. How do we determine if the chi-squared value is significant?
4. What is the role of degrees of freedom in the chi-squared test?
5. How would different expected percentages affect the chi-squared statistic?

Tip: When calculating expected counts, always ensure the total expected counts sum to the total observed count.