Billyjoe claims that his new card shuffling machine shuffles a deck of card very thoroughly so the deck is completely random. Amyjoe is not sure she believes him and comes up with a test for Billyjoe's claim. Amyjoe knows that if the deck is randomly shuffled and she draws the top card from the deck, the probability it is an ace is the probability it is a face card is and the probability it is a numeric card is . She executes the following plan: shuffle the entire deck, draw the top card and note what it is (ace, face or numeric). Do that 130 times (each time the entire deck is shuffled). Then compare the frequencies of ace, face and numeric cards with the probability distribution. Amyjoe and Billyjoe proceed to do the experiment and obtain the following frequencies: after 130 shuffles, they saw 15 aces, 28 face cards and 87 numeric cards. Perform an appropriate hypothesis test to determine if Billyjoe's shuffling machine really is dealing random decks of cards. Test at the 0.025 significance level.