The percentage of high school graduates applying to multiple

The percentage of high school graduates applying to multiple colleges has been increasing over the past several years. According to the National Association for College Admission Counseling, 29% of high school students applied to seven or more colleges in 2011. A random sample of 350 high school graduates in 2013 was selected and 84 of them applied to seven or more colleges. Construct a 90% confidence interval to estimate the actual proportion of high school graduates that applied to seven or more colleges in 2013. What is the margin of error for this sample? Is there evidence that this proportion has changed since 2011 based on this sample? Verify your results with PHStat.

Solution

Sample proportion p = 84/350 = 0.24

b)

z for 90% = 1.645

Margin of error = z * sqrt(p(1-p)/n)

= 1.645 * sqrt(0.24 * 0.76 / 350)

= 0.038 Answer

a)

Confidence Interval : (0.29 - 0.038 , 0.29 + 0.038)

= ( 0.252 , 0.328) Answer

c)

No