The World Health Organization estimates that 5% of all adults in sub-Saharan Africa are living with HIV/AIDS. A survey takes a random sample of 1600 adults from all over sub-Saharan Africa and finds that 84 have HIV/AIDS. What is the approximate sampling distribution of the proportion who live with HIV/AIDS?

Question

Quizplus · Accepted Answer

The sampling distribution of the proportion can be approximated by a normal distribution with mean equal to the population proportion (p) and standard deviation equal to sqrt[p(1-p)/n], where n is the sample size. Given p = 0.05 and n = 1600, the mean of the distribution is 0.05 and the standard deviation is sqrt[0.05*0.95/1600] = 0.0054. Therefore, the correct approximation is N(0.0500, 0.0054).

The World Health Organization Estimates That 5% of All Adults