You are tasked with construction of a survey to estimate the proportions of the 6.741 billion world population living with HIV/AIDS. A past survey obtained results for 2005 show nearly 27 million people living with HIV/AIDS.
a) How many people do you need to sample in order to construct a 95% confidence interval that is within 2 million of the parameter?
b) From past surveys on HIV/AIDS there is considered to be a 5% probability that your results will be much to low - below 10% or more. There is also a 3% chance that your survey will be much too high - over 10% or more. Based on the previous results what is the probability that your results will be either too low or too high? What probability rule did you use to answer this question?
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