Standard +0.3 This is a straightforward hypothesis test using normal approximation to Poisson with clearly stated hypotheses. Students must recognize λ=44 allows normal approximation, apply continuity correction, calculate z-score, and compare to critical value. While it requires multiple steps, each is standard procedure for S2 level with no conceptual surprises or novel problem-solving required.
3 Flies stick to wet paint at random points. The average number of flies is 2 per square metre. A wall with area \(22 \mathrm {~m} ^ { 2 }\) is painted with a new type of paint which the manufacturer claims is fly-repellent. It is found that 27 flies stick to this wall. Use a suitable approximation to test the manufacturer's claim at the \(1 \%\) significance level. Take the null hypothesis to be \(\mu = 44\), where \(\mu\) is the population mean.
Test statistic \(z = \frac{27.5 - 44}{\sqrt{44}} = -2.487\)
B1, M1, A1 (marks)
For correct \(H_1\); For standardisation attempt with or without cc or \(\sqrt{}\); For correct test statistic
\(CV: z = +\) or \(-2.326\)
B1 (mark)
Correct CV or finding area on LHS of -2.487 and comparing with 1%
Claim justified
B1 ft (5 marks total)
Correct conclusion, compare + with + or with -
$H_0: \mu = 44$
$H_1: \mu < 44$
Test statistic $z = \frac{27.5 - 44}{\sqrt{44}} = -2.487$ | B1, M1, A1 (marks) | For correct $H_1$; For standardisation attempt with or without cc or $\sqrt{}$; For correct test statistic
$CV: z = +$ or $-2.326$ | B1 (mark) | Correct CV or finding area on LHS of -2.487 and comparing with 1%
Claim justified | B1 ft (5 marks total) | Correct conclusion, compare + with + or with -
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3 Flies stick to wet paint at random points. The average number of flies is 2 per square metre. A wall with area $22 \mathrm {~m} ^ { 2 }$ is painted with a new type of paint which the manufacturer claims is fly-repellent. It is found that 27 flies stick to this wall. Use a suitable approximation to test the manufacturer's claim at the $1 \%$ significance level. Take the null hypothesis to be $\mu = 44$, where $\mu$ is the population mean.
\hfill \mbox{\textit{CAIE S2 2005 Q3 [5]}}