A human resources department is comparing two employee training programs to see if they lead to different pass rates on a required certification exam. They randomly select two groups of employees. In Program A, 16 out of 20 employees passed the exam. In Program B, 30 out of 40 employees passed. Are the basic conditions met to conduct a 2-proportion hypothesis test?

• A. Yes, the basic conditions are met.
• B. No, the basic conditions are not met.
• C. There is not enough information to answer the question.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the requirements for conducting a 2-proportion hypothesis test. The basic conditions include: (1) Random sampling, (2) Independence between the two groups, and (3) Sufficient sample size to ensure the sampling distribution of the sample proportions is approximately normal.
2. Step 2: Check the random sampling condition. Verify whether the employees in both groups were randomly selected. The problem states that the groups were randomly selected, so this condition is satisfied.
3. Step 3: Check the independence condition. Ensure that the two groups (Program A and Program B) are independent of each other. The problem does not explicitly mention whether the groups are independent, so this needs to be clarified.
4. Step 4: Check the sample size condition. For each group, calculate the expected number of successes and failures using the formulas: \( n_1 \cdot p_1 \), \( n_1 \cdot (1 - p_1) \), \( n_2 \cdot p_2 \), and \( n_2 \cdot (1 - p_2) \), where \( n_1 \) and \( n_2 \) are the sample sizes, and \( p_1 \) and \( p_2 \) are the sample proportions. Ensure all these values are greater than or equal to 5.
5. Step 5: Based on the above checks, determine if all conditions are met. If any condition is not satisfied or there is insufficient information (e.g., independence is unclear), then the basic conditions for conducting a 2-proportion hypothesis test are not met.