Question

A university administrator writes a report in which he states that at 45% of all students have driven while under the influence of drugs or alcohol.  Many others think the correct percent is less than 45%.

To resolve the issue, a random sample of 400 students is obtained and it is found that 156 or 39% admit that they have driven under the influence of drugs or alcohol.  Here are some results:

x	N	Sample p	Z-value	p-value
156	400	0.39	-2.41	0.008

What conclusion should be made?

	A.	There is insufficient evidence to conclude that the true proportion of students that has driven under the influence is less than 39%.
	B.	There is insufficient evidence to conclude that the true proportion of students that has driven under the influence is less than 45%.
	C.	There is sufficient evidence to  conclude that the true proportion of students that has driven under the influence appears to be less than 39%.
	D.	Without stated null and alternative hypotheses, a conclusion cannot be drawn.
	E.	There is sufficient evidence to conclude that the true proportion of students that has driven under the influence appears to be less than 45%.

Answer 1

Here we're testing Ho: p=0.45 vs Ha: p<0.45

Here the p-value is 0.008.

Thus we can reject Ho, and conclude that:

E.	There is sufficient evidence to conclude that the true proportion of students that has driven under the influence appears to be less than 45%.