Tasting Experiment - Can Friend Distinguish Pepsi from Coke?

[musicgold]

Hi,

One of my friends was bragging that he could distinguish between Coke and Pepsi drinks just by taste. So I challenged him to taste drinks from 10 glasses and identify them as a Pepsi or a Coke. In five of the ten randomly arranged glasses, I had poured Pepsi and Coke in the remaining. He could correctly identify the drinks in seven out of the 10 glasses (C = 7, where C means correctly identified).

Now I am trying to analyze the result; however, I am not clear on two issues.

1. What should be the null hypothesis in this experiment, C = 0 or C = 10?

2. Which distribution to use? My guess is that I should be using a binomial distribution for this experiment, as there are only two outcomes for each trial. If that is correct, how do I find the p value of the experiment?
I know that the binomial distribution is a special case of the normal distribution, but not sure whether should I use the critical value tables for the normal distribution or t-distributions.

Thanks,

MG

 

[CRGreathouse]

The usual idea would be to show that you can't reject the null hypothesis that p = 0.5 (that your friend just guessed well). You then add up the chance that the friend guessed 10, 9, 8, and 7 correctly (using the binomial distribution) and see how likely that is. If it's below 5% (or 100% - c, where c is your confidence -- I used the standard 95%) then you can't reject the possibility that your friend guessed well but can't tell them apart.