Answer :
Final answer:
The conditions for inference needed to conduct a z-test for one proportion are met, including the random condition, the 10% condition, and the large counts condition, based on the information given.
Therefore, the correct answer is: option "Yes, the random, 10%, and large counts conditions are all met.
Explanation:
To determine if the conditions for inference are met for conducting a z-test for one proportion, we must check the following conditions:
- Random: The sample of Americans must be chosen randomly.
- 10% Condition: The sample size must be no more than 10% of the entire population.
- Large Counts Condition: Both np and n(1-p) must be at least 10, where n is the sample size and p is the proportion in question.
Assuming the financial advisor has selected a random sample, the random condition is met.
As the population of American adults is large, well over 1500, the 10% condition is met.
For the large counts condition, we can calculate np = 150 x 0.8 = 120 and n(1-p) = 150 x 0.2 = 30.
Since both of these are greater than 10, the large counts condition is also met. Therefore, all conditions for conducting a z-test for one proportion are satisfied.