Standard +0.3 This is a straightforward one-tailed Poisson hypothesis test requiring students to set up H₀: λ=12 vs H₁: λ>12, find P(X≥19) using tables or calculation, and compare to 10% significance level. It's slightly above average difficulty due to being a hypothesis test (not just calculation) and requiring correct interpretation, but follows a standard S2 procedure with no conceptual complications.
5 A temporary job is advertised annually. The number of applicants for the job is a random variable which is known from many years' experience to have a distribution \(\operatorname { Po } ( 12 )\). In 2010 there were 19 applicants for the job. Test, at the 10\% significance level, whether there is evidence of an increase in the mean number of applicants for the job.
Explicitly compare \(P(\ge 19)\) with 0.1, or \(P(\le 18)\) with 0.9
\(Or: CR \text{ is } \ge 18, p = 0.063\)
A1
\(\ge 18\) and 0.063 stated
\(19 \ge 18\)
B1
Explicit comparison of CV (right-hand CR) with 19
Reject \(H_0\). Significant evidence of increase in mean number of applicants
M1 FT
"Reject", FT, needs correct method and comparison, e.g. not from \(\le 19\) or \(= 19\), withhold if inconsistent
7
Interpreted in context, acknowledge uncertainty
$H_0: \lambda = 12$; $H_1: \lambda > 12$ | B2 | Both correct; B2. Allow $\mu$. One error, B1, but not $x$, $r$ etc.
$Either: P(\ge 19) = 1 - P(\le 18) = 1 - 0.9626 = 0.0374$ | M1 | $Po(12)$ stated or implied, e.g. 0.9787
| A1 | 0.0374, or 0.9626 if compared with 0.9
| B1 | Explicitly compare $P(\ge 19)$ with 0.1, or $P(\le 18)$ with 0.9
$Or: CR \text{ is } \ge 18, p = 0.063$ | A1 | $\ge 18$ and 0.063 stated
$19 \ge 18$ | B1 | Explicit comparison of CV (right-hand CR) with 19
**Reject $H_0$. Significant evidence of increase in mean number of applicants** | M1 FT | "Reject", FT, needs correct method and comparison, e.g. not from $\le 19$ or $= 19$, withhold if inconsistent
| | 7 | Interpreted in context, acknowledge uncertainty
5 A temporary job is advertised annually. The number of applicants for the job is a random variable which is known from many years' experience to have a distribution $\operatorname { Po } ( 12 )$. In 2010 there were 19 applicants for the job. Test, at the 10\% significance level, whether there is evidence of an increase in the mean number of applicants for the job.
\hfill \mbox{\textit{OCR S2 2011 Q5 [7]}}