| course | course_year | question_number | tags | title | year | |||
|---|---|---|---|---|---|---|---|---|
Statistics |
IB |
69 |
|
3.I.8C |
2007 |
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
[Hint: You may wish to use some of the following percentage points:
$\left.\begin{array}{c|ccccccccc}\text { Distribution } & \chi_{1}^{2} & \chi_{2}^{2} & \chi_{3}^{2} & \chi_{4}^{2} & t_{1} & t_{2} & t_{3} & t_{4} \ \hline 90 % \text { percentile } & 2 \cdot 71 & 4 \cdot 61 & 6.25 & 7 \cdot 78 & 3 \cdot 08 & 1.89 & 1 \cdot 64 & 1.53 \ 95 % \text { percentile } & 3.84 & 5.99 & 7 \cdot 81 & 9 \cdot 49 & 6 \cdot 31 & 2.92 & 2 \cdot 35 & 2 \cdot 13\end{array}\right]$