Light bulbs are sold in packets of 3 but some of the bulbs are defective. A sample of 256 packets yields the following figures for the number of defectives in a packet:

\begin{tabular}{l|cccc} No. of defectives & 0 & 1 & 2 & 3 \ \hline No. of packets & 116 & 94 & 40 & 6 \end{tabular}

Test the hypothesis that each bulb has a constant (but unknown) probability $\theta$ of being defective independently of all other bulbs.

[Hint: You may wish to use some of the following percentage points:

$\left.\begin{array}{c|ccccccccc}\text { Distribution } & \chi_{1}^{2} & \chi_{2}^{2} & \chi_{3}^{2} & \chi_{4}^{2} & t_{1} & t_{2} & t_{3} & t_{4} \\ \hline 90 \% \text { percentile } & 2 \cdot 71 & 4 \cdot 61 & 6.25 & 7 \cdot 78 & 3 \cdot 08 & 1.89 & 1 \cdot 64 & 1.53 \\ 95 \% \text { percentile } & 3.84 & 5.99 & 7 \cdot 81 & 9 \cdot 49 & 6 \cdot 31 & 2.92 & 2 \cdot 35 & 2 \cdot 13\end{array}\right]$