Moderate -0.3 This is a straightforward one-tailed binomial hypothesis test with clear setup (n=20, x=2, p=1/4, 10% significance). It requires standard procedure: stating H₀ and H₁, calculating P(X≤2) under H₀, and comparing to 0.05 (one-tail). The only mild challenge is recognizing this is one-tailed (testing for decrease only, since x=2 is below expected 5), but the calculation itself is routine S2 material requiring no novel insight.
3. In a sack containing a large number of beads \(\frac { 1 } { 4 }\) are coloured gold and the remainder are of different colours. A group of children use some of the beads in a craft lesson and do not replace them. Afterwards the teacher wishes to know whether or not the proportion of gold beads left in the sack has changed. He selects a random sample of 20 beads and finds that 2 of them are coloured gold.
Stating your hypotheses clearly test, at the \(10 \%\) level of significance, whether or not there is evidence that the proportion of gold beads has changed.
3. In a sack containing a large number of beads $\frac { 1 } { 4 }$ are coloured gold and the remainder are of different colours. A group of children use some of the beads in a craft lesson and do not replace them. Afterwards the teacher wishes to know whether or not the proportion of gold beads left in the sack has changed. He selects a random sample of 20 beads and finds that 2 of them are coloured gold.
Stating your hypotheses clearly test, at the $10 \%$ level of significance, whether or not there is evidence that the proportion of gold beads has changed.\\
\hfill \mbox{\textit{Edexcel S2 2001 Q3 [7]}}