I'm currently reviewing for a statistics final, and have been using the practice final supplied in class to do so. I understand the material, the problem lies in a difference between the answer I got (which was, by the way, the same as the one reached by a math tutor I asked) and the one the teacher supplied. In case I missed some important detail, I'll supply everything we were provided.
A sample of n=200 college students is asked if they believe in extraterrestrial life and 120 of these students say that they do. The data are used to test:
Ho: p=0.5 vs Ha: P>0.5
Where p is the population proportion of college students who say they believe in extraterrestrial life. The following information is provided:
95% Confidence Interval=(0.532105,0.667895)
What is the correct description of the area that equals the p-value for this problem?
a.) The area to the right of 0.60 under a standard normal curve
b.) The area to the right of 2.83 under a standard normal curve
c.) The area to the right of -2.83 under the normal standard curve.
d.) The area between 0.532105 and 0.667895 under a normal standard curve.
The answer I got was b, with a and d being eliminated at possible answers because the numbers they're based on doesn't concern the Z-value, on which the area in question is based. Now, to my understanding, it would be the area to the right of 2.83, as the p-value is greater than 0.5, rather than being less than. The teacher, however, supplied the answer as being c, and I want to clarify which it is, rather than going into the exam unprepared. Any help, explanation, even agreement is greatly appreciated.