A card-dealing machine deals spades (1), hearts (2), clubs (3), and diamonds (4) at random as if from an infinite deck. In a randomness check, 1,600 cards were dealt and counted. The results are shown below. To test if the poker-dealing machine deals cards at random, the null and alternative hypotheses are ________.

Question

A card-dealing machine deals spades (1), hearts (2), clubs (3), and diamonds (4) at random as if from an infinite deck. In a randomness check, 1,600 cards were dealt and counted. The results are shown below.  To test if the poker-dealing machine deals cards at random, the null and alternative hypotheses are ________.

Quizplus · Accepted Answer

The null hypothesis should state that the population proportions for each card suit are equal to 0.25 (since there are 4 suits, each suit should represent 0.25 or 25% of the population). The alternative hypothesis should state that not all population proportions are equal to 0.25, implying that the machine is not random. Therefore, only choice B correctly states the null and alternative hypothesis.

A Card-Dealing Machine Deals Spades (1), Hearts (2), Clubs (3)