I have read that 20% of undergraduate students experience food insecurity sometime during each academic year. I wish to test if this is true at a particular university. I plan the following experiment. I will randomly sample 100 students at the university and compute the proportion of them who have experienced food insecurity during the last year; this proportion is p-hat. If p-hat ≤ 0.12 or p-hat ≥ 0.28, I will decide that the proportion of students experiencing food insecurity during the last year was not equal to 0.20. Otherwise, I will decide I cannot conclude it was different from 0.20. When I run the trial, I find 15 of the 100 students experienced food insecurity during the previous year, so p-hat = 0.15. Take the following probabilities as given; you do not need to check them. They provide all the information you need in order to answer the first section of questions. Let p be the proportion of students who experience food insecurity each year at the university. If p=0.20, P(p.hat≤ 0.12) = 0.025, P(p.hat≥ 0.28) = 0.025, and P(p-hat≤ 0.15) = 0.11. If p=0.30, P(p.hat≤ 0.12) = 0, P(p.hat≥ 0.28) = 0.68, and P(p-hat≤ 0.15) = 0.0005. What is the null hypothesis being tested? What is the alternate hypothesis? What is the test statistic? What is the rejection region for our test? What is α for our test? What is the power if the probability of insecurity is 0.30? What is the p-value of our result?

I have read that 20% of undergraduate students experience food insecurity sometime during each academic year. I wish to test if this is true at a particular university. I plan the following experiment. I will randomly sample 100 students at the university and compute the proportion of them who have experienced food insecurity during the last year; this proportion is p-hat. If p-hat ≤ 0.12 or p-hat ≥ 0.28, I will decide that the proportion of students experiencing food insecurity during the last year was not equal to 0.20. Otherwise, I will decide I cannot conclude it was different from 0.20.

When I run the trial, I find 15 of the 100 students experienced food insecurity during the previous year, so p-hat = 0.15.

Take the following probabilities as given; you do not need to check them. They provide all the information you need in order to answer the first section of questions. Let p be the proportion of students who experience food insecurity each year at the university. If p=0.20, P(p.hat≤ 0.12) = 0.025, P(p.hat≥ 0.28) = 0.025, and P(p-hat≤ 0.15) = 0.11. If p=0.30, P(p.hat≤ 0.12) = 0, P(p.hat≥ 0.28) = 0.68, and P(p-hat≤ 0.15) = 0.0005.