To solve this problem, we need to complete the table and conduct a chi-square test to determine if the observed results significantly differ from the expected results.

Step-by-Step Solution:

1. Calculate Differences (o - e):

   • For AA: $60 - 70 = -10$
   • For A: $20 - 20 = 0$
   • For B: $20 - 10 = 10$

2. Square of Differences $(o - e)^2$:

   • For AA: $(-10)^2 = 100$
   • For A: $0^2 = 0$
   • For B: $10^2 = 100$

3. $(o - e)^2 / e$ Calculation:

   • For AA: $100 / 70 = 1.43$
   • For A: $0 / 20 = 0$
   • For B: $100 / 10 = 10$

4. Sum $(\Sigma)$:

   • Add up the values in the $(o - e)^2 / e$ column: $1.43 + 0 + 10 = 11.43$

Degrees of Freedom:

• Since there are 3 categories, the degrees of freedom $A = 3 - 1 = 2$.

Chi-Square Critical Value:

• For $p = 0.05$ and $\text{df} = 2$, the critical value from the chi-square table is $5.99$.

Decision:

• Compare the calculated chi-square value (11.43) with the critical value (5.99).
• Since $11.43 > 5.99$, we reject the null hypothesis.

Final Answer:

$\text{11.4,reject}$

Would you like more details on any step, or do you have further questions?

Here are five follow-up questions related to this topic:

1. What would happen if the observed values were closer to the expected values?
2. How would you interpret a situation where the chi-square value is less than the critical value?
3. How do degrees of freedom affect the chi-square test?
4. What are other common uses of the chi-square test besides goodness of fit?
5. How would the conclusion change if we used a different significance level, such as $p = 0.01$?

Tip: When interpreting chi-square results, always compare your calculated chi-square value with the critical value for your chosen significance level and degrees of freedom.