A Spinner Is Mounted on a Piece of Cardboard Divided $\frac { 1 } { 6 }$

Multiple Choice

A spinner is mounted on a piece of cardboard divided into six areas of equal size. Each of the six areas is a different color (blue, yellow, red, green, white and orange) . When the spinner is spun, each color should be selected by the spinner approximately $\frac { 1 } { 6 }$ of the time. A student suspects that a certain spinner is defective. The suspected spinner is spun 90 times. The results are shown below. Find the critical value $\chi _ { 0 } ^ { 2 }$ to test the student's claim. Use $\alpha = 0.10$ .
$\begin{array} { l | c c c c c c } \text { Color } & \text { Blue } & \text { Yellow } &\text { Red }&\text { Green } & \text { White } & \text {Orange } \\ \hline \text { Frequency } & 12 & 11 & 16 & 19 & 17 & 15\end{array}$

A) 9.236
B) 1.610
C) 10.645
D) 11.071