3. Recently, the Maryland Gaming Commission has received complaints from numerou

Question

3. Recently, the Maryland Gaming Commission has received complaints from numerous patrons of the Maryland Live! Casino in Hanover, Maryland, regarding the dice game known as Craps. The complaints generally state that the dice at the casino appear to be "loaded." meaning unfair. To investigate, you select a random sample of dice from the casino and test whether each die is fair, meaning whether each of the six sides is equally likely. The results for one die follow: VALUE 10 20 32 35 31 a. State the null and alternative hypotheses associated with the test. b. What is the calculated value of the associated test statistic? c. If the level of significance equals 0.01, what is the critical value of the associated test statistic? d. State your decision regarding the null hypothesis. e. State your conclusion (meaning, describe what the decision means in this problem).

Explanation / Answer

The chi-square goodness-of-fit test evaluates these hypotheses:

·    H0 : Data follow a multinomial distribution with certain proportions

·    H1 : Data do not follow a multinomial distribution with certain proportions

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: f

Test Contribution
Category Observed Proportion Expected to Chi-Sq
1 10 0.166667 25 9.00
2 20 0.166667 25 1.00
3 32 0.166667 25 1.96
4 35 0.166667 25 4.00
5 31 0.166667 25 1.44
6 22 0.166667 25 0.36

N DF Chi-Sq P-Value
150 5 17.76 0.003

P-value <0.05 we reject the null hypothesis

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