A pokerdealing machine is supposed to deal cards at random a

A poker-dealing machine is supposed to deal cards at random, as if from an infinite deck.

In a test, you counted 1600 cards, and observed the following:

Spades 404

Hearts 420

Diamonds 400

Clubs 376

You want to determine whether the machine is malfunctioning an is dealing non-randomly.

a. What is the null hypothesis?

b. What is the alternative hypothesis?

c. What are the expected values?

d. Calculate the chi-squared value

e. What do you conclude?

Solution

1. 1600 cards, 4 suits – ¼ chance of a suit being drawn. ¼ of 1600 =400.

Observed

Expected

(o-e)²/e

404

400

.04

420

400

1

400

400

0

376

400

1.44

X² = 2.48

Degrees of freedom = 3

Critical value = 7.82

Because 2.48 is below 7.82, we can accept that the cards are being sorted randomly.

Ho :the machine isnot malfunctioning ( There are the same value for each)

H1 : the machine is malfunctioning ( there are not the same value for each)