In a random sample of students who took the SAT Reasoning college entrance exam twice, it was found that 427 of the respondents had paid for coaching courses and that the remaining 2733 had not.

What is the upper bound on the 95% confidence interval for the proportion of coaching among the students who retake the SAT?
in Statistics Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

This is a binary situation. We use np to find the mean and np(1-p) to find the variance, where n is the dataset size and p the probability of a randomly selected student who had paid for coaching. We can then apply a normal distribution to determine the confidence interval (CI).

n=427+2733=3160, p=427/3160=0.1351 approx. Mean, μ=427, σ2=np(1-p)=369.3, standard deviation, σ=19.22 approx. The critical value for 95% CI is 5% (0.025) two-tailed significance. The Z-score for 95% is 1.96. To find the upper bound X, we use (X-μ)/σ=Z, X=μ+σZ=427+19.22×1.96=464.67 approx.

Upper bound is 464 (the largest integer lower than 464.67).

by Top Rated User (894k points)

Related questions

0 answers
1 answer
asked Jan 29, 2015 in Statistics Answers by VLanham Level 1 User (420 points) | 320 views
Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
86,882 questions
93,634 answers
24,243 users