Moderate -0.3 This is a straightforward hypothesis test for a binomial proportion at a non-standard significance level (10%). It requires setting up H₀: p=0.25 vs H₁: p≠0.25, calculating P(X≤2) for B(20, 0.25), and comparing to 0.05 for a two-tailed test. The calculation is routine and the context is clear, making it slightly easier than average, though the two-tailed nature and 10% level require careful attention.
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. She 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. [7]
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. She 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. [7]
\hfill \mbox{\textit{Edexcel S2 Q3 [7]}}