High School

We appreciate your visit to The cafeteria manager at a high school with 910 students and 75 teachers is considering adding a baked potato bar to the lunch menu The. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

The cafeteria manager at a high school with 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?

A. Yes, the conditions for inference are met.
B. No, the 10% condition is not met.
C. No, the randomness condition is not met.
D. No, the Large Counts Condition is not met.

Answer :

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 [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex], 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

Thanks for taking the time to read The cafeteria manager at a high school with 910 students and 75 teachers is considering adding a baked potato bar to the lunch menu The. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada