Question

A national organization sets out to investigate the change in prevalence of HIV since the last census in 2010. A total of 4706 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%. A) Is the sample size large enough to justify the use of the Z formula? Show all calculations to support the answer B) Test if the proportion of the prevalence of HIV has changed (H0 is equal to 7.5%). Use alpha = 0.05. Include all hypothesis testing steps and do not use the plus-four method. C). Calculate the 95% two-sided confidence interval for p and make a conclusion about H0. Do not use the plus-four method.

Answer 1

The estimated proportion is

A) WE see that both greater than 10. And assume that the sample size is less than 5% of the population size. So we can use z-distribution.

B)We have to test

The test statistic is

The P-value of the test is

Since the P-value is , we reject the null hypothesis. Strong evidence to support the claim that the prevalence of HIV has changed.

C) The confidence interval for proportion is

The 95% two-sided confidence interval for proportion is

We can see that . Hence reject the null hypothesis.