Suppose the Proportion of Sophomores at a Particular College Who $p _ { s }$

Suppose the proportion of sophomores at a particular college who purchased used textbooks in the past year is $p _ { s }$ and the proportion of freshmen at the college who purchased used textbooks in the past year is $p _ { f }$ . A study found a $90 \%$ confidence interval for $p _ { s } - p _ { f }$ is $( 0.234,0.421 )$ . Give an interpretation of this confidence interval.

A) We are $90 \%$ confident that at this college the proportion of sophomores who bought used textbooks is between $23.4 \%$ and $42.1 \%$ higher than the proportion of freshmen who bought used textbooks.
B) We are $90 \%$ confident that at this college the proportion of freshmen who bought used textbooks is between $23.4 \%$ and $42.1 \%$ higher than the proportion of sophomores who bought used textbooks.
C) We are $90 \%$ confident that sophomores at this college bought between $23.4 \%$ and $42.1 \%$ more used textbooks than freshmen.
D) We know that $90 \%$ of all random samples done on the population will show that the proportion of sophomores who bought used textbooks is between $23.4 \%$ and $42.1 \%$ higher than the proportion of freshmen who bought used textbooks.
E) We know that $90 \%$ of sophomores bought between $23.4 \%$ and $42.1 \%$ more used textbooks than freshmen at this college.