How can I justify Null Conclusion based on Confidence Interval ? My question is as follows:
*An ad claims people prefer S coffee over P coffee. The person randomly samples 80 coffee drinkers and finds 43 prefer S coffee.  The person concludes the claim is probably not true.  How did the person justify this?
(a) 46% is not in the 95% CI
(b) 46% is in the 95% CI
(c) 50% is not in the 95% CI
(d) 50% is in the 95% CI*
I set the Null Hypothesis as S =.5 (there is no difference in the people who like S coffee over P coffee.  Therefore Ha = S >  0.5. (more people prefer S)
I compute the Z value using the proportions formula for z and get $z = 0.53$.  I look this up in the normal z chart for a right-tailed test and find p-value to be about 30%.  I would accept the Null based on such a high p-value.  In other words I would think the ad's claim is not true.  HOWEVER, it would be based on the z value, or corresponding p-value, and not any of the items listed in the question about 43% or 50% being in or out of the 95% CI.
What am I missing here?
 A: You're correct that up until the point that that the answer options are offered, the question is framed as a hypothesis test, so that's the most obvious way to approach that set-up.
However, at the point you see the answer options it's clear that the question is asking you to look at the confidence interval for the proportion (to see if it contains the case specified under the null) rather than conduct the hypothesis test. 
The confidence interval could be thought of as a set of values for the parameter that are (in a very particular sense) "consistent" with the data-set.
As soon as you see those options, it should be clear that if you don't think in terms of the confidence interval, you'll have trouble answering the question.
An aside that doesn't impact what you need to do here: The author(s) of the question seem to implicitly assume that the two procedures would yield the same conclusion, but in in the most commonly taught tests vs intervals for proportions it's not necessarily the case that they will yield the same conclusion. They nearly always give the same conclusion (and they do here), but it's not always so. It's quite possible to choose a different pair of procedures for this situation that will always correspond, though. In almost every other situation you'd learn in an elementary course, they always correspond. Many books and web-pages explicitly state that they always correspond (see here for one example of many; it's wrong on that point but you might find the explanations otherwise useful).
