A researcher is estimating the population proportion of U.S. adults ages 18 to 24 who have had an HIV test. The estimate must be accurate within 2% of the population proportion with 90% confidence. Find the minimum sample size needed when

(1) No preliminary estimate is available and

(2) A previous survey found that 31% of U.S. adults ages 18 to 24 have had an HIV test.

a. Identify p̂, q̂, z_c, and E. If p̂ is unknown, use 0.5.

b. Use p̂, q̂, z_c, and E to find the minimum sample size n.

c. Determine how many U.S. adults ages 18 to 24 should be included in the sample.