Based on the NYC Department of Health Community Health Survey in 2010, a 95% confidence interval for the proportion of New Yorkers who were tested for HIV in the past 12 months is (29.9%, 32.9%). If the population size is 6 million in 2010, with 95% confidence, we know that at least how many New Yorkers were tested for HIV within the past 12 months?

Question

Mathematics

Angus

17 September, 01:05

Based on the NYC Department of Health Community Health Survey in 2010, a 95% confidence interval for the proportion of New Yorkers who were tested for HIV in the past 12 months is (29.9%, 32.9%). If the population size is 6 million in 2010, with 95% confidence, we know that at least how many New Yorkers were tested for HIV within the past 12 months?

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Gardner · Answer 1

With 95% confidence, at least 1,794,000 were tested for HIV within the past 12 months

Step-by-step explanation:

The lower bound of the confidence interval is 29.9%.

So, with 95% confidence, we know that at least 29.9% of the New York population tested for HIV.

Out of 6 million, that is:

0.299*6000000 = 1,794,000

With 95% confidence, at least 1,794,000 were tested for HIV within the past 12 months