Question

Instructions: Read each scenario below, and then answer the questions that follow. Don’t forget to write the appropriate category labels in the empty boxes for each table.

One of the more interesting applications of the c² test is to examine issues of fairness and cheating in games of chance. Since such games usually involve wagering, there is an incentive for people to try to rig the games, and allegations of missing cards, "loaded" dice, and "sticky" roulette wheels are all too common. Take the example of dice. Most dice used in wagering have six sides, with each side having a value of one, two, three, four, five, or six. If the die being used is fair, then the chance of any particular number coming up is the same: 1 in 6. However, if the die is loaded, then certain numbers will have a greater likelihood of appearing, while others will have a lower likelihood.

1. It’s Friday night at the Tunisian Nights Casino, and renowned gambler Jeremy Turner is having a fantastic night at the blackjack table. Out of all of the 36 games played, he beats the dealer 28 times and loses to the dealer 8 times. You are convinced that he has been counting cards. The c² test can be used to estimate the likelihood that the number of wins Turner has had occurred by chance. Note: the total for both the observed and expected will be the total number of games he has played.

                 

Blackjack data

a = .05	Game result		Total
Observed
Expected

df = ______________   critical χ² = _________________ χ² = ___________________ Significant? Y or N

Interpret the results of the χ² analysis.

2. After Turner finishes at the Blackjack table, you (the casino’s statistician) follow him to a craps table. In two hours of playing, he's racked up $30,000 in winnings and is showing no sign of stopping. Crowds are gathering around him to watch his streak, and he is telling everyone within earshot that his good luck is due to the fact that he's using the casino's lucky pair of "bruiser dice," so named because one is black and the other blue. Unbeknownst to Turner, however, you have been quietly watching his rolls and marking down the values of each roll, noting the values of the black and blue dice separately. After 60 rolls, you have become convinced that the blue die is loaded: you’ve recorded the blue die rolling a one 16-times; a two 5-times; a three 9-times, a four 7-times; a five 6-times; and a six 17-times. The c² test can be used to estimate the likelihood that the values observed on the blue die occurred by chance.

Craps data

a = .05	Dice Rolls						Total
Observed
Expected

df = ______________   critical χ²= _________________   χ²= ___________________ Significant? Y or N

Interpret the results of the χ² analysis.

3. Based on the results of the χ² analyses, would you inform the owner of the casino of your discoveries and recommend Turner be thrown out? In other words, is Turner cheating? Why/why not?

Answer 1

From the observed data y observed frequency o Expected propostien Expected frequency if (0-1) 5556 28 18.00 0-5000 8 5.556 18. DO 0.500 chi-square test statistic x= [(0-E)? E critical value 3.8415 lend of significance x=0.05 Degree of freedom kal 2-1-1 P-value = 0.0009 Decision : p-value cai Reject Ho (2 ) 10-6)/E Observed Expected Expected frequency o proportion brequency 16 0.167 10.00 3.600 5 0.167 10.00 2-500 9 0.167 10.00 DIDO 7 0.167 10.00 D. 900 6 0.167 10.00 1600 11 0.167 1000 4900 chi-square test statistic x² = {10-E² - 13.600 £ critical value - 11.0705 Level et significance &=0.05 Degree of freedom kala 6-1=5 0.0184 p-value Decision - P-value <a, Reject to yes, need be thrown out Turnex to (3) + will this answer helpful for you Thope please give up-vote for Work,