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 48 times and note the following results: Face "1" "2" "3" "4" "5" "6"
Observed count 12 8 4 5 8 11

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

Identify Ha:
Ha: every p ≠ 1/6, implying the dice are fair.
Ha: at least one p ≠ 1/6, implying the dice are fair.
Ha: every p ≠ 1/6, implying the dice are unfair.
Ha: at least one p≠ 1/6, implying the dice are unfair.

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

(c) Is the cell count condition met?
No, because some cells have less than 30 observed counts.
Yes, because the expected cell count is at least 5 for all cells.
Yes, because the expected cell count is close to the observed cell count for all cells.
No, because some cells have less than 10 observed counts.

(d) Calculate the contribution to the test statistic for the dice side with number "6": (Use 4 decimals):

(e) The test statistic is χ2 = 6.250. What is the P-value? (Use 4 decimals.)

(f) What is the appropriate test conclusion, for = 0.05?
There is sufficient evidence the dice are unfair.
There is sufficient evidence the dice are fair.
There is insufficient evidence the dice are fair.
There is insufficient evidence the dice are unfair.