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?