Reference no: EM132415841

According to an article, a survey of about 13,000 students showed the fewest number of students having sex since the survey was started: about 52% of surveyed students had never had sexual intercourse, compared with 46% in the starting year. If we assume the population proportion to be roughly 0.5, the margin of error will be 2√0.5(1 - 0.5)/n = 1/√n, where n is the sample size.

(a) To the nearest thousandth, find the approximate error margin for students in general (n = 13,000). (Round your answer to three decimal places.)

(b) Based on the sample proportion 0.52 and the margin of error from part (a), is the conclusion, that the majority of teens are not sexually active, justified?

a. Yes

b. No

(c) Find the approximate error margin for boys, assuming that half of the 13,000 students (or 6,500) were boys. (Round your answer to three decimal places.)

(d) Find the approximate error margin for Hispanics, assuming that 13% of the 13,000 students were Hispanic. (Round your answer to three decimal places.)

(e) The article reports that proportions who were sexually active dropped substantially for whites and African-Americans, but for Hispanics, the proportion only dropped from 0.53 to 0.52. Should we be convinced that the Hispanics' rate dropped at all? Based on sample proportion 0.52 and margin of error from part (d), tell whether or not 0.53 is still a plausible value for Hispanics' population proportion.

a. 0.53 is still plausible, and so we should not be convinced that the rate dropped at all.

b. 0.53 is not plausible, and so we are convinced that the rate has dropped.

(f) In general, are we better able to pinpoint a change with larger samples or with smaller samples?

a. larger samples

b. smaller samples