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. At the 5% significance level,the critical value is ______.

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.  At the 5% significance level,the critical value is ______.

Quizplus · Accepted Answer

To find the critical value at the 5% significance level, we need to use the chi-square distribution with (number of categories - 1) degrees of freedom. In this case, we have 4 categories, so the degrees of freedom is 4-1=3. Using a chi-square distribution table (or calculator), we find that the critical value at the 5% level with 3 degrees of freedom is 7.815. Therefore, the answer is B.

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