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. For the goodness-of-fit test,the degrees of freedom 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.  For the goodness-of-fit test,the degrees of freedom are ____.

Quizplus · Accepted Answer

The goodness-of-fit test is used to determine whether observed data follows a particular theoretical distribution. In this case, we are testing whether the observed frequencies of each suit match the expected frequencies for a uniform distribution (which assumes that each suit has an equal chance of being dealt).

Since there are four possible outcomes (spades, hearts, clubs, diamonds), there are three degrees of freedom (df = number of possible outcomes - 1). Therefore, the best choice is B.

A Card-Dealing Machine Deals Spades (1),hearts (2),clubs (3),and Diamonds (4)at