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A national organization sets out to investigate the change in prevalence of HIV since the last...

A national organization sets out to investigate the change in prevalence of HIV since the last census in 2010. A total of 4,706 participants were interviewed and a total of 468 responses were confirmed to be HIV positive. Assume that the data from the census indicated that the prevalence of HIV in the particular population was 7.5%. Is the sample size large enough to justify the use of the Z formula? Show your calculation to support your answer. (3 points) Test if the proportion of the prevalence of HIV has changed (H0 is equal to 7.5%). Use ∝ = 0.05. Note: Remember to include all hypothesis testing steps and do not use the plus-four method. (10 points) Calculate the 95% two-sided confidence interval for p and make a conclusion about H0. (4 points). Note: Do not use the plus-four method.

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