In randomized, double-blind clinical trials of a new vaccine, monkeys were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the second dose, 125 of 663 subjects in the experimental group (group 1) experienced drowsiness as a side effect. After the second dose, 82 of 544 of the subjects in the control group (group 2) experienced drowsiness as a side effect. Does the evidence suggest that a higher proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the $\alpha=0.01$ level of significance?

Verify the model requirements. Select all that apply.
A. $n_{1} \hat{p}_{1}\left(1-\hat{p}_{1}\right) \geq 10$ and $n_{2} \hat{p}_{2}\left(1-\hat{p}_{2}\right) \geq 10$
B. The sample size is more than $5 \%$ of the population size for each sample.
C. The data come from a population that is normally distributed.
D. The samples are independent.
E. The samples are dependent.
F. The sample size is less than $5 \%$ of the population size for each sample.

Step 1 ：First, we need to calculate the sample proportions of subjects who experienced drowsiness in group 1 and group 2, denoted as \( \hat{p}_{1} \) and \( \hat{p}_{2} \) respectively.

Step 2 ：For group 1, \( n_{1} = 663 \) and \( x_{1} = 125 \). So, \( \hat{p}_{1} = \frac{x_{1}}{n_{1}} = \frac{125}{663} = 0.1885 \).

Step 3 ：For group 2, \( n_{2} = 544 \) and \( x_{2} = 82 \). So, \( \hat{p}_{2} = \frac{x_{2}}{n_{2}} = \frac{82}{544} = 0.1507 \).

Step 4 ：Next, we need to check if the conditions for a hypothesis test for the difference between two proportions are satisfied.

Step 5 ：Condition A is that the sample sizes are large enough for the Central Limit Theorem to apply. This is usually satisfied if \( n_{1} \hat{p}_{1}(1-\hat{p}_{1}) \geq 10 \) and \( n_{2} \hat{p}_{2}(1-\hat{p}_{2}) \geq 10 \).

Step 6 ：For group 1, \( n_{1} \hat{p}_{1}(1-\hat{p}_{1}) = 663 * 0.1885 * (1 - 0.1885) = 101.3 \), which is greater than 10.

Step 7 ：For group 2, \( n_{2} \hat{p}_{2}(1-\hat{p}_{2}) = 544 * 0.1507 * (1 - 0.1507) = 69.8 \), which is also greater than 10.

Step 8 ：So, condition A is satisfied.

Step 9 ：Condition B is that the samples are less than 10% of the population, to ensure independence within each sample. We don't know the exact population size, but given that the subjects are monkeys and the sample sizes are 663 and 544, it's reasonable to assume that the sample sizes are less than 10% of the population size. So, condition B is also satisfied.

Step 10 ：Condition D is that the samples are independent. In the given problem, the monkeys were randomly divided into two groups, so the samples are independent. So, condition D is also satisfied.

Step 11 ：The conditions C, E, and F are not requirements for a hypothesis test for the difference between two proportions, so they are not applicable.

Step 12 ：Therefore, the model requirements that are satisfied are A, B, and D.

Step 13 ：Final Answer: \(\boxed{\text{A, B, D}}\)