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%. Required:
Test if the proportion of the prevalence of HIV has changed (is equal to 7.5%). Use α = 0.05.

As can be seen, there has been a rise in the proportion of the population with HIV positive, from 7.5% to 9.94%.

Step-by-step explanation:

Given that a national organization sets out to investigate the change in prevalence of HIV since the last census in 2010, ya total of 4,706 participants were interviewed and a total of 468 responses were confirmed to be HIV positive, assuming that the data from the census indicated that the prevalence of HIV in the particular population was 7.5%, to determine if the proportion of the prevalence of HIV has changed (is equal to 7.5%) the following calculation should be performed:

4706 = 100

468 = X

468 x 100/4706 = X

46,800 / 4,706 = X

9.94 = X

Therefore, as can be seen, there has been a rise in the proportion of the population with HIV positive, from 7.5% to 9.94%.