Question

The cafeteria manager at a high school that has 910 students and 75 teachers is considering adding a baked potato
bar to the lunch menu. The manager randomly surveys 90 students and 25 teachers, and finds that 50 of the 90
students and 13 of the 25 teachers would purchase from the potato bar. The manager constructs a 99% confidence
interval for the difference in the proportions of students and teachers who would purchase lunch on the day the
potato bar option is available. Are the conditions for inference met?
Yes, the conditions for inference are met.
No, the 10% condition is not met.
O No, the randomness condition is not met.
No, the Large Counts Condition is not met.

Answer 1

Using the Central Limit Theorem, it is found that the correct option regarding whether the conditions for inference are met is:

Yes, the conditions for inference are met.

What is the condition for inference by the Central Limit Theorem?

By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1 - p)}{n}}$, as long as $np \geq 10$ and $n(1 - p) \geq 10$, that is, there are at least 10 failures and 10 successes in each sample.

In this problem, for each of the two samples, there are at least 10 failures and 10 successes, that is, the conditions are met, hence the correct option is:

Yes, the conditions for inference are met.

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213