DATA 606 Presentation

(a) Is this sample a representative sample from the population of all high school seniors in the US? Explain your reasoning.
No. This is an optional online survey and the sample is taken only from the students who took SAT. Additionally only the students who are interested in taking survey have completed it. We can check whether this survey met the independence and success-failure conditions for the Central Limit Theorem applies, and it's a normal distribution.

• Sample observations are independent.
• We are expected to see least 10 successes and 10 failures

n <- 1509
p <- .55
(success <- n*p)

[1] 829.95

(failure <- n*(1-p))

[1] 679.05

By these conditions, we can say that central limit theorem conditions are met. But this is an optional online survey, only the high school seniors who are interested in survey are completing it.

(b) Let's suppose the conditions for inference are met. Even if your answer to part (a) indicated that 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 this interval in context.

se <-  sqrt((p*(1-p))/n)
z <- qnorm(.95)
confidence_interval_upper <- p+z*se
confidence_interval_lower <- p-z*se

c(confidence_interval_lower,confidence_interval_upper)

[1] 0.5289346 0.5710654

We are 90% confident that 53% to 57% of high school seniors who took the SAT are fairly certain that they will participate in a study abroad program in college.

d) 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?

Yes. The interval lies entirely above 50%.