You play a game of dice at the state fair, but suspect the dice may have been ri

Question

You play a game of dice at the state fair, but suspect the dice may have been rigged. You observe the game owner rolling the dice 90 times and note the following results:

(a) Which hypotheses should be used to test if the dice are fair:
Identify H0:

___ H0: p1 = p2 = p3 = p4 = p5 = p6 = 0, implying the dice are unfair.

___ H0: p1 = p2 = p3 = p4 = p5 = p6 = 1/6, implying the dice are fair.     

___ H0: p1 = p2 = p3 = p4 = p5 = p6 = 0, implying the dice are fair.

___ H0: p1 = p2 = p3 = p4 = p5 = p6 = 1/6, implying the dice are unfair.

Identify Ha:

___ Ha: every p 1/6, implying the dice are unfair.

___ Ha: at least one p 1/6, implying the dice are fair.     

___ Ha: at least one p 1/6, implying the dice are unfair.

___ Ha: every p 1/6, implying the dice are fair.

(b) What is the expected count for each side of the dice?  

(c) Is the cell count condition met?

___ Yes, because the expected cell count is at least 5 for all cells.

___ No, because some cells have less than 10 observed counts.     

___ No, because some cells have less than 30 observed counts.

___ Yes, because the expected cell count is close to the observed cell count for all cells.

(d) Calculate the contribution to the test statistic for the dice side with number "1": (Use 4 decimals):  

(e) The full test statistic is 2 = 15.067. What is the P-value? (Use 4 decimals.)  

(f) What is the appropriate test conclusion, for = 0.05?

___ There is insufficient evidence the dice are unfair.

___ There is sufficient evidence the dice are unfair.     

___ There is insufficient evidence the dice are fair.

___ There is sufficient evidence the dice are fair.

Explanation / Answer

a)  H0: p1 = p2 = p3 = p4 = p5 = p6 = 1/6, implying the dice are fair.

Ha: at least one p 1/6, implying the dice are unfair

b)

expected count for each side of the dice =90/6 =15

c) Yes, because the expected cell count is at least 5 for all cells.

d) contribution to the test statistic for the dice side with number "1" =(O-E)2/E =(19-15)2/15 =1.0667

e) p value =0.0101

f)as p value is less then 0.05 level

_ There is sufficient evidence the dice are unfair.  

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