An article in Engineering Horizons (Spring 1990, p. 26) reported that 117 of 484 new engineering graduates were planning to continue studying for an advanced degree. Consider this as a random sample of the 1990 graduating class.
(a) Find a 90% confidence interval on the proportion of such graduates planning to continue their education.
(b) Find a 95% confidence interval on the proportion of such graduates planning to continue their education.
(c) Compare your answers to parts (a) and (b) and explain why they are the same or different.
(d) Could you use either of these confidence intervals to determine whether the proportion is actually 0.25? Explain your answer. Hint: Use the normal approximation to the binomial.