Please help. A drug manufacturer claims that 13% of the population of South Africa is living with HIV. As a World Health Organization researcher, you collect evidence to test this claim. You use statistical techniques to sample 125 random residents of South Africa and find that 20 of them test positive for HIV.

You plan to simulate one sample of 125 residents by randomly selecting 125 integers between 1 and 100.
From your actual sample of 125 residents, what proportion of the sample has HIV?

What do the randomly selected numbers represent? Why did you pick 125 of them?

What assigned numbers indicate a simulated resident has HIV?

2. You plan to run 100 simulations, each with a random sample of 125 residents.
What do you think the true mean population proportion from the 100 simulations would be close to? Explain why.

Is this a simulation of an observational study or an experimental study? Explain why.

The margin of error for this study is about 0.06 or 6% around the population proportion. Are you able to support the claim of the drug manufacturer? Explain why or why not.

What could be done to make the margin of error smaller and get a better sample of the population? Why does that make sense?