6.11 Study Abroad. A survey on 1,509 high school seniors who took the SAT and who completed an optional web survey between April 25 and April 30, 2007 shows that 55% of high school seniors are fairly certain that they will participate in a study abroad program in college.

  1. Is this sample a representative sample from the population of all high school seniors in the US? Explain your reasoning.

    • The sample is NOT representative of the population. Not all high schoolers take the SAT; some take the ACT instead. It would be a good sample representation of all US high school seniors who took the SAT.

  2. Let’s suppose the conditions of inference are met. Even if your answer to part(a) indicated tthat this approach would not be reliable, this analysis may still be interesting to carry out (though not report). Construct a 90% confidence interval for the proportion of high school seniors(of those who took the SAT) who are fairly certain they will participate in a study abroad program in college, and interpret the interval in context.

n <- 1509
p.hat <- .55
z.star <- 1.65
SE <- sqrt((p.hat*(1-p.hat))/n)
CI.LOWER <- p.hat - (z.star*SE)
CI.UPPER <- p.hat + (z.star*SE)
CI <- c(CI.LOWER, CI.UPPER)
CI
## [1] 0.5288687 0.5711313
#our CI is (.5289, .5711)

  1. What does 90% confidence mean?

    • It means that we are 90% confident that 53-57 percent of high schools seniors are fairly certain that they would like to participate in a study abroad program. We can say that 90% if random samples would give us 90% CI that includes the true proportion (.55).

  2. Based on this interval, would it be appropriate to claim that the majority of high school seniors are fairly certain that they will participate in a study abroad program in college?

    • We can claim that the majority of HS seniors are fairly certain that they will participate in a study above program. What we found is that the interval is over 50% (majority).