Each Side of a Standard Six-Sided Die Should Appear Approximately $$\frac { 1 } { 6 }$$

Multiple Choice

Each side of a standard six-sided die should appear approximately $$\frac { 1 } { 6 }$$ of the time when the die is rolled. A player suspects that a certain die is loaded. The suspected die is rolled 90 times. The results are shown below.
Find the critical value χ $$x _ { 0 } ^ { 2 }$$ to test the playerʹs claim. Use $$\alpha = 0.10 .$$ $$\begin{array} { l | c c c c c c } \text { Number } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Frequency } & 11 & 15 & 12 & 16 & 17 & 19\end{array}$$

A) 9.236
B) 1.610
C) 12.833
D) 11.071