Following Are Observed Frequencies $H _ { 0 } : p _ { 1 } = 0.35 , p _ { 2 } = 0.2$

Multiple Choice

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.35 , p _ { 2 } = 0.2$ , $p _ { 3 } = 0.15 , p 4 = 0.15 , p _ { 5 } = 0.15$ .
$\begin{array}{l|lllll}\text { Category } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Observed } & 38 & 26 & 22 & 4 & 16\end{array}$

Compute the value of $\chi ^ { 2 }$ .

A) 14.332
B) 13.277
C) 15.086
D) 12.356