Moderate -0.3 This is a straightforward one-tailed binomial hypothesis test with clearly stated hypotheses (H₀: p=0.24, H₁: p<0.24), requiring calculation of P(X≤2) under B(25,0.24) and comparison to 5%. While it involves multiple binomial probability calculations, it's a standard textbook procedure with no conceptual challenges or novel problem-solving required, making it slightly easier than average.
4 In this question you should not use an approximating distribution.
At an election in Menham last year, \(24 \%\) of voters supported the Today Party. A student wishes to test whether support for the Today Party has decreased since last year. He chooses a random sample of 25 voters in Menham and finds that exactly 2 of them say that they support the Today Party.
Test at the 5\% significance level whether support for the Today Party has decreased.
[Evidence to reject \(H_0\).] There is sufficient evidence to suggest that the support for the Today Party has decreased.
A1FT
FT *their* probability. In context, not definite, no contradictions. SC: if \(H_1: p \neq 0.24\) and compare with 0.025; max B0 M1 A1 M1 A0
Total: 5
## Question 4:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $H_0: p = 0.24$; $H_1: p < 0.24$ | B1 | |
| $P(X \leq 2) = 0.76^{25} + 25\times0.76^{24}\times0.24 + {}^{25}C_2\times0.76^{23}\times0.24^2$ or $0.0010479 + 0.0082732 + 0.0313513$ | M1 | Expression must be seen. No end errors. |
| $= 0.0407$ | A1 | SC B1 for unsupported 0.0407 |
| $0.0407 < 0.05$ | M1 | For valid comparison |
| [Evidence to reject $H_0$.] There is sufficient evidence to suggest that the support for the Today Party has decreased. | A1FT | FT *their* probability. In context, not definite, no contradictions. SC: if $H_1: p \neq 0.24$ and compare with 0.025; max **B0 M1 A1 M1 A0** |
| **Total: 5** | | |
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4 In this question you should not use an approximating distribution.\\
At an election in Menham last year, $24 \%$ of voters supported the Today Party. A student wishes to test whether support for the Today Party has decreased since last year. He chooses a random sample of 25 voters in Menham and finds that exactly 2 of them say that they support the Today Party.
Test at the 5\% significance level whether support for the Today Party has decreased.\\
\hfill \mbox{\textit{CAIE S2 2024 Q4 [5]}}