A deck of Zener cards has 5 different cards, shown below. There are 200 of each in the deck.

An individual that claims to have telepathic abilities is presented with 100 cards facedown and attempts to demonstrate their telepathy by guessing what symbol each card shows. Of course their telepathic powers are not perfect, but they manage to successfully guess 30 of the 100 cards. Is this sufficient evidence of some sort of telepathy?

1.Determine an appropriate null and alternative hypothesis. Your null hypothesis should reflect skepticism that the subject is telepathic. (What proportion of cards would you guess correctly if you chose randomly?) What's the population here? (This is a little more abstract than our typical population.) What about the sample? The variable of interest?

Find the value of the appropriate test statistic.

Calculate the P-value.